Hey geeks, welcome to the next article of this series on signals and systems. In the previous lecture, we saw the basic types of convolution and learned about convolution in MATLAB. This time, we are going to enhance some concepts about it by learning about the properties of convolution and by adding some important pieces of information about the same topic. Have a look at today’s concepts:
What are some basic properties of convolution?
What is the correlation?
Discuss some types of correlation and their implementation in MATLAB.
What is the difference between convolution and correlation?
How convolution is used in different areas of science and how different departments are using this technique to control the parameters efficiently.
Once you have a clear idea of linear/circular convolution, you can easily understand its properties. These convolution techniques that we have discussed till now are used in many fields of signal processing, and if you have a grip on their concepts, you can easily use it anywhere they are applicable.
There are three main properties of linear convolution:
Commutative property
Associative property
Distributive property
This property says that linear convolution is commutative. It means that no matter what the sequence of the signal or function is that is involved in linear convolution, the result will remain the same.
Mathematically,
x(n)*h(n) = h(n)*x(n)
It means whether you convolve the second function and multiply it with the first one or vice versa, the result will remain the same.
We can replace a succession of Linear-Time Invariant systems with a single system pulse response that is equal to the convolution of the impulse responses of the individual LTI systems using the associative property of convolution.
Mathematically,
y(n) = [x(n)*h1(n)] *h2(n) = x(n)*[h1(n)*h2(n)]
This property implies when there are more than two signals involved in convolution.
This property also depends upon more than two functions. It is a combination of addition and convolution of the signals. It says that the result of the addition of two signals and then convoluting them with the third one is equal to the addition result of the convolution of each signal separately from the third signal. If it is not clear to you with this statement, have a look at the equation.
Mathematically,
x(n)*[h1(n)+h2(n)] = [x(n)*h1(n)] +[x(n)*h2(n)]
Correlation is the measure of similarities between two signals, functions, or waveforms that are usually used in signal processing. In other fields of science, a correlation has other meanings. Yet, in signals and systems, correlation compares two signals and provides the similarity. It is introduced as:
“In signals and systems, correlation is the procedure to find the similarity between the values of two signals, and it also measures the extent of this similarity in such a way that zero correlation means no similarity and vice versa.”
This is an important procedure, as in signals and systems, all the work is done with the help of waveforms or signals, and correlation helps to figure out the extent of similarity between them.
Let’s take two signals out of one is x(t) and the other is y(t), then the correlation, denoted by r, is obtained by using the following formula:
rxy(τ)= ∫∞−∞x(t)⋅y(t−τ) dt
Keep in mind that there is a difference between the relation of x to y and y to x. Therefore, changing the position with the r means we have to change the values on the other side of the equation as well. As you can see, the correlation is done by using the dot sign between the signals.
If you have the idea of convolution that we discussed in the previous lecture, then you must be familiar with the other components of the formula as well.
Based on how the correlation is solved in different ways, the correlation is broadly divided into two different types:
Autocorrelation
Cross-correlation
The first type of correlation is the one in which the signal is compared with itself. Here is the formula for it:
rxx(τ)=∫∞−∞x(t)x⋆(t−τ) dt
Now the question arises, how can a signal be compared with itself to find the similarity? Well, as you can see clearly in the formula, the signal x is correlated with the time-shifted version of the signal itself. In this way, we can say, auto-correlation is a uni-signal procedure.
Code
x=[1 2 4 7]
h=[4 7 8 1]
a=xcorr(x,h)
subplot(2,1,1)
stem(a)
title('Auto-Correlation')
xlabel('Time / The Engineering Projects')
ylabel('Amplitude')
grid on;
Output
The measure of similarity or coherence between one signal and the time-delayed version of another signal is defined as the cross-correlation between two different signals, functions, or waveforms. The degree of relatedness between one signal and the time-delayed version of another signal is indicated by cross-correlation.
Code
t=2:0.1:1
x=[1 2 4 7]
h=[4 7 8 1]
a=xcorr(x,h)
subplot(2,1,1)
stem(a)
title('Correlation')
xlabel('Time / The Engineering Projects')
ylabel('Amplitude')
grid on;
Output
You can see it is a simple program with two signals and by using a simple formula of correlation as:
xcorr(i,j)
Where i and j are the signals, we can have an accurate correlation between the signals. There are some cases in which more than two entries are possible in the same formula, and MATLAB works best in that too.
Always keep in mind that we are using the stem command to show the signal in the discrete format, but you can also have the results in the continuous time format by simply putting the value of the result (here a is the result) in the plot format to get the desired result.
Convolution |
Correlation |
|
Introduction |
Overlapping two signals to have the third one. |
Finding the relation between two signals |
Denotion |
It is denoted by a (*) sign between signals |
It is denoted by a dot (.) between signals. |
The number of signals |
Always two or more |
Maybe 1 or more |
Types |
Linear convolution, circular convolution |
Auto-correlation, cross-correlation |
Functions in MATLAB |
conv(a,b), cconv(a,b) |
xcorr(a,a) ,xcorr(a,b) |
You will also see some other differences between these two at some points, but according to the point of view of the course we are studying, these applications are more than enough to understand. It is an important question that is usually asked during exams, and you must go through each of these points to clear up the concept.
As we have said earlier, convolution is an important topic in signals and systems. Now, we are moving toward its applications so that you will get an idea of why we were emphasizing the importance of this topic. Here are some important and interesting applications of convolution techniques in signals and systems.
Image processing
Customizing patterns of signals
Audio processing
Polynomial multiplication
Artificial intelligence
Optics
We are going through each of these points consecutively because if you are familiar with the convolution technique as we have given the details in the previous sections, you are going to enjoy each of these. We are not going deep into the discussion because the deep discussion is not in the context of this course. You just have to understand the information and you will be amazed to know how simple topics can be useful in different ways.
First of all, let us discuss the way in which convolution changes the quality of the picture in any way you want. To understand it well, let’s discuss some points.
Image processing is based on tiny pixels, and the number of pixels decides the quality of the picture.
Operations on the images in a computer system are processed in the form of 2D arrays.
The processing of images is done by using matrices of different sizes, and the smaller one is called the Kernal, and its size is important in this process. Through the convolution process, we can change the edge privilege (as shown in the picture), and in this way, we can change the edge style with this technique.
In the same way, convolution is used to sharpen or smooth the image according to the requirements. Another application of convolution in image processing is to blur the image to maintain the security or any other intention behind the convolution.
As we have mentioned in the theoretical section before this, we can deal with the impulse response of the signals in convolution and if a person has deep knowledge of it, he can customize the pattern effectively using signals according to their own choice.
Similar to image processing, audio processing can also be controlled with the help of this technique. Audio signals can be mixed to have the third one, or you can simply use them to enhance the quality of your sound signals.
"Convolution reverb" is the technical term for the process of digitally simulating reverberation. It allows you to convolve the known impulse response of an area with that of the desired sound to simulate the reverberation effect of a specific area.
You have probably seen the multiplication of polynomials in your early classes, and you must be wondering why we are mentioning this term here. Keep in mind that polynomials may be very complex at a high level and it may become a headache to solve them correctly. Luckily, convolution can solve such multiplication within seconds by converting these polynomials into a matrix and solving them accordingly. In the end, when we have the values of each polynomial, one can also use the calculation further to use them for other purposes. Have a deep look at our description. We are talking about the multiplication of polynomials, but in real life, the convolution is carried out instead of multiplication, and we get the desired results.
Convolution are used in artificial intelligence and e all now it is an emerging technique in which many people are working. Artificial intelligence works by using different types of networks of elements, and these networks are associated with the parameters that are known as “weight”. These weights are somehow associated with the convolution process, and in this way, we can change the influence of a particular node at a particular output.
In the field of optics, where the major function is with the help of light and small details matter a lot, convolution is an effective way to change the parameters through which light is controlled. In this way, experts know how to control the light with the help of convolution.
The diffraction pattern in optics depends mainly upon two types of patterns of light:
Slits
Circular shape
And by carefully controlling these two parameters through convolution and other techniques, experts are doing great in the field of optics.
It was an interesting lecture today where we learned some important properties of convolution and gained a piece of great knowledge about correlation as well. For me, learning about the application of convolution was an interesting way to highlight the importance of my learning. You must go through some other points on the same topics as your homework. Now we are moving towards a relatively complex topic but do not worry, we are going to learn this step by step by mentioning all the basic and necessary information. In the next lecture, you will come across some different types of transforms in signal and system processing, and you will understand these if you have a little information about the time domain and frequency domain. So go through these, and have a great day.
Hey pupils, Welcome to another lecture of this series on signals and systems, and this is the time to learn an interesting topic in which you are going to learn about the convolution of the signals. In the previous sessions, we have learned basic operations on the signals, and this time, you are going to know the convolution of the signals and different criteria that are related to this topic. Have a quick view of the concepts that will be clarified in this lecture:
What is convolution?
What are some basic types of convolution?
How can you define the properties of linear convolution?
How can you implement convolution in MATLAB using function and without function?
What is the difference between linear and circular convolution?
Convolution is a mathematical operation and it is widely used in signals and systems by using a minimum of two signals at a time. The basic definition of convolution is:
The term "convolution" refers to a mathematical process combining two signals by overlapping them to produce a third signal.
It is important because it establishes a connection between the system's input signal and the impulse response of the system, which determines the system's output, which is utilized to provide a relationship within the LTI system.
Before going into details of the convolution, you must have the idea of shifting and scaling that we have discussed before in this series. Let’s recall them.
"Time shifting" refers to moving a signal forward or backward in time. The time variable in the function is multiplied by the shift or subtracted from it to do this."
Hence, convolution is an integral function that is used to measure the amount of overlap of one function when it is shifted over the other function.
If the definition of convolution is clear to you, then you can easily understand the formula for it.
We all know that there are two types of signals and, therefore, there is a different representation of the formula of convolution in each type.
Convolution of a continuous-time system:
Where,
y(t) = convoluted result
x(t)= 1st function
h(t)= 2nd function
Convolution for a discrete-time system:
Similar to the 1st case,
y(n) = convoluted result
x(n)= 1st function
h(n)= 2nd function
The steric sign here represents convolution, and it is the most important part of this formula. Do not be confused with the symbols of t and k in continuous and discrete signals, respectively. These are the dummy variables of the result so that the input and output representation must not change.
We are not going into details of the derivation but for the clear concepts, let’s solve the example to have practice.
Basically, there are two types of convolution that are used in signal and system. These are
Linear convolution
Circular convolution
A brief description of each of them is given next:
This is the basic type of convolution and is defined as:
“The calculation of the output of any Linear-Time Invariant (LTI) system, given that system's input and impulse response, is done with the help of a mathematical procedure known as linear convolution.”
Till now, the properties and procedures that we have discussed were related to linear convolutions. One thing that must be kept in mind is, that the arrow on the values of x(t) and h(t) indicates the zero position of the function. If this arrow is not specified, then by default, the first value is the zero value.
You will find different formulas to have the convolution of signals, but here, we are providing you with the basic and easiest way to solve the convolution without any confusion. Just follow these simple steps to get the convolution.
Replace T with t
Time reversal in h(t)= h(-t)
Time shifting in h(t)= h(t-t)
Multiplication of h(t-t) with x(t)
Integration of the result by taking the limits from minus infinity to infinity
Keep in mind, in all the steps, the value of x(t) remains the same and just t is replaced by t i.e, time reversal and time shifting do not apply to x(t) while you are using the convolution.
The other type that I found more interesting in the convolution of signals is circular convolution. This type can be performed using two different methods, and by observing the procedure of each type, you will understand why this type is called “Circular” convolution. The total number of samples in circular convolution is equal to the maximum number of values in x(t) or h(t). Have a look at both of these:
Concentric circular convolution
Matrix circular convolution
We are going to discuss both of them in the next section.
Here, you need a circle for each signal or function. In this way, you will have two circles. Follow the steps from the beginning as mentioned below:
Draw a big circle on the page and write the values of x(t) on it at regular intervals.
Draw a relatively small circle inside the first one and write all the values of h(t) on it at the same regular intervals.
Multiply the respective values of both the circles and at the end, add them all. You will get a number.
Now, draw the same circle once again but this time, you have to move the internal circle (the one with h(t) values) one place anti-clockwise and then repeat the above procedure till you get all the values.
The matrix multiplication, as the name implies, consists of two matrices having the values of x(t) and h(t) respectively. The simple steps involved in this method are:
One of the given sequences is repeated, one sample at a time, to produce an N X N matrix.
The other sequence is shown as a column matrix.
The outcome of circular convolution is obtained by multiplying two matrices.
Here comes the action. You have seen that there were different ways of convolution, and honestly speaking, these procedures are long yet easy. MATLAB has built-in functions for convolution so that you may get the answer to long and time-taking calculations in just a bit. You just have to simply input the values, and tell MATLAB that you want to do the convolution of this signal. Let’s implement all the discussions in MATLAB and get the instant and authentic result of convolution there.
Fire up your MATLAB software.
Go to live editor or command window to write the code.
Click the “Run” button.
Save program.
There is a built-in function in MATLAB that is super easy to use, and you do not have to go deep into the procedure. You just have to simply provide the input signals and use the convolution function. If x and h are two signals that have the values, then using this function, you can easily convolute them as
conv(x,h)
At the end, you just have to simply put this value in the y variable so that you can plot or stem it easily. Here is the code and output.
Code | Output |
x=[1 2 3]; h=[1 4 6 8]; y=conv(x,h); stem(y) title('Convolution using function') xlabel('Time / The Engineering Projects') ylabel('Amplitude') grid on; |
|
It may come into your exam that you are required to perform the linear convolution but without the help of function. Usually, it happens when the instructor wants to check the knowledge and concept of the student. So here is a simple program for this.
Code | Output |
x=[1 2 3]; h=[1 4 6 8]; m1=length(x); m2=length(y); subplot(2,2,1) stem(x) title('x') xlabel('Time') grid on; subplot(2,2,2) stem(y) title('h') xlabel('Time ') ylabel('Amplitude') grid on; a=[x, zeros(1,m1)]; b=[h, zeros(1,m2)]; for i=1;(m2+m1-1) y(i)=0; for j=1:m1 if(i-j+1)>0 ylabel('Amplitude') y(i)=y(i)+a(j)*b(i-j+1); end end end subplot(2,2,3); title('Convolution without function') xlabel('Time / The Engineering Projects') ylabel('Amplitude') grid on; |
|
Circular convolution can also be done with the help of function and without it as well. Of course, it is easier to use the function, but in some cases, if you do not want to use the function, it is also possible to do it without the help of the function. The difference between the formulas is, that the circular convolution involves the third parameter as well. This value is obtained when the total number of values of signals is compared and we get the maximum value. For a practice point of view and to clear up the concepts about the topic, we are also using it without any function.
Code | Output |
x=[2 2] h=[1 1 1] l1=length(x) l2=length(h) N=max(l1,l2) a=cconv(x,h,N) subplot(2,1,1) stem(a) title('Circular Convolution with Function') xlabel('Time / The Engineering Projects') ylabel('Amplitude') grid on; x=[x zeros(1,N-l1)] h=[h zeros(1,N-l2)] y=zeros(1,N) for n=1:N for m=1:N j=mod(n-m,N) j=j+1 y=y+x(m)*h(j) end end subplot(2,1,2) stem(y); title('Circular Convolution Without Function') xlabel('Time / The Engineering Projects') ylabel('Amplitude') grid on; |
|
Similar to some other functions, length is also a function of MATLAB that stores the output of the number of values that are fed into this function. Let's suppose if the number of elements on the x-axis in a signal is ten and we feed the signal into this function, then it will provide us with the length of 10. It may seem simple, but in complex signals where a hundred or thousand values in a signal are used, this function proves very helpful.
Have you observed a function “Max” in the code? It is a built-in function of MATLAB that compares the entries and provides you with the entry (signal in our case) with the maximum number of values. Usually, the answer is then fed into a variable so that we can use the result of this max function anywhere without any difficulty.
For your information, we must share that there is another function named "min", and as you can guess, it does the opposite work. Two or more values are given to this function as well and it compares and then provides the minimum value between these two. It may seem a small task but if used correctly, these functions give us control of many useful things by using them in our program.
Linear Convolution | Circular Convolution | |
Complexity | Less Complex | More Complex |
Shifting | Linear Shifting | Circular Shifting |
Numbers of samples | N1+N2-1 | Max(N1, N2) |
Types | Not common types | Concentric circular convolution, Matrix circular convolution |
Formula in MATLAB | conv(a,b) | cconv(a,b) |
Convolution is an important topic in signals and systems as it is used to overlap the two signals on each other in such a way that a third signal is obtained that is different from the first two. We have read some important properties of linear convolution and also seen the performance of each type with and without the function in MATLAB. The purpose of providing the program of convolution without function is to clearly describe the concept and the method of convolution. If you have any type of question regarding the topic, you can contact us.
Hello Pupils, We are learning about signals and systems, and till now we have learned some basic information regarding signals, but we know a little about systems till now. We have learned about the system in our previous lectures. To have a clear concept, we have arranged this tutorial in which we are studying the systems and their classification. Have a quick glance at today’s topics:
What is a system?
What are the various types of systems?
What is the principle of homogeneity?
What is the principle of superposition?
How can we compare each type while keeping their differences in mind?
To keep things simple, we’ll also have examples of some of these signals. Yet, the first thing that we are going to do is to revise the basic definition of the system so that we may move forward.
A system is a closed connection between the input signal and the output. All the procedures and techniques required to convert the input into output are called the system, and if we talk critically, then the basic definition of a system is:
“A system is a collection of components that, when interconnected, provide a signal that is proportional to the signal that was fed into the system.”
To understand, keep in mind, that the system has the input where the data is fed, then different procedures take palace on that data, and as a result of this procedure, we get the output from the system.
As with signals, systems also have some types, and these types are clearly classified for convenience. We will go through some basic types and will try to have a clear concept through discussion and examples.
There are different ways to define the linearity of the system, but the easiest one is, that a system is called linear only if it follows:
Principles of homogeneity
Principle of Superposition
We’ll define both of them one after the other in detail.
According to the concept of homogeneity, a system that produces an output y(t) for an input x(t) must also provide an output ay(t) for an input ax. This is the condition that must be met for the system to be considered homogeneous (t).
According to the concept of superposition:
“A system that produces an output of y1(t) for the input of x1(t) and output of y2(t) for the input of x2(t) must create an output of [y1(t) + y2(t)] for the input of [x1(t) + x2(t)]. Similarly, [y1(t) + y2(t)] for the input of [x1(t)], and implies any number of different signals in the system. "
Well, is it confusing? Do not worry because we are discussing it in simple words. Consider the case when the system has more than one signal in it. If we provide it with 3 signals (let’s say) at the input, then the output contains the collective effect of all the signals that we were expecting from each and every signal by adding them.
It may make no sense at the time because every person, after using their commonsense, can make this decision on their own, but keep in mind that these types of principles are highly effective in solving the complex problem of calculations.
As a result, when we plot the graph of a linear system, we find a simple and clear graph that is usually straight in line. It is the reason behind calling them “linear”. It is usually easy to deal with the linear system as compared to the other type that is non-linear. The reason behind this will be discussed in just a bit. Before that, have a look at the diagram given below:
On the other hand, if the system does not obey the principles of superposition and homogeneity, then it is called non-linear. It is not possible to develop a general differential equation of finite order that can be utilized as the mathematical model for all systems when dealing with nonlinear systems; this is because such an equation would be impossible to solve. This is due to the fact that there are numerous distinct paths via which nonlinearities might emerge, and these paths cannot all be mathematically expressed using the same form. In addition to this, it is essential to keep in mind that the concept of superposition cannot be applied to nonlinear systems.
Let’s talk about a very simple and obvious type of system. A system is called a continuous-time signal if the input given to it, and the output obtained from it, both are continuous-time signals. The operations done on the input do not change the form of the input signals and hence the output is not affected in its shape and type.
A simple example of a continuous-time signal is an amplifier in which the input is analog in the form of voice. Different procedures occur inside the system (amplifier), and from the output, an amplified voice (analog signal) is obtained from it.
As you are expecting, a discrete-time system is one in which the input given to the system and the output obtained from the system, after different procedures, are in the form of discrete-time signals. If in any case, the system changes the signal from discrete to continuous, then it will not be a discrete-time system.
Micro-processor is an example of a discrete-time signal because all the processes that occur in the micro-processor are based on just two numbers that are zero and one and the output, after different operations, remains in the same format.
In some cases, the same results can be obtained from the output of the system that was fed into its input signal, and such systems are termed invertible systems, as the name implies. We define them as:
“A system is said to be an invertible system if it is designed in such a way that the input, that is fed into the system goes through some changes and these changes can be converted into the original signal again by using the different procedure and the input is equal to the output.”
Practically, an invertible system is obtained by using a system in which, in addition to the simple system, an inverter or any other device, that has the opposite mechanism is cascaded to obtain the same input and output.
The system in which the input and output are not equal is called non-insertable. We define them as:
“A system is said to be non-invertible if the effect of the system, exerted on the input signal, can not be inverted. No matter which procedure you are following inside the system, you will get different inputs and outputs. “
Time-Variant systems are those whose output depends upon time. We know that every signal has time on the x-axis but keep in mind, in a time-variant system, a signal depends upon the change in time.
The example given below represents the case of a time-variant system:
y(n)= x(-n)
The system is said to be time-invariant if the output of the system does not depend upon the time of the system.
Consider an example in which the output is called y(t) and the input is represented as x(t). Then the equation given below presents the time-invariant system:
y(t)=x(t)+x(t-1)
Here is another type of system. We all know that static means motionless or unchanging condition. A static system is one that depends upon a particular result at a particular time and it does not have any relationship with the previous or future results.
“A static system is the one that depends upon the present situation only and does not have any mechanism to store the past or future value because it does not need to store these values”.
𝑐(𝑡) = 𝑟(𝑡)
𝑐(𝑡) = 2𝑟2(𝑡)
In these examples, the whole system depends upon the time at a particular instant, and it does not have any concern with the previous or upcoming value. This will be more clear when you look at the example of the dynamic signal in just a bit.
Dynamic means anything that is not stationary. In the case of signals, the dynamic signals are the ones that depend upon the present, past, and future values of the signals. Have a look at the definition:
“A dynamic system is one that can not be achieved by using the present values of the signals only; instead, they also depend upon the future and past values, and therefore, they require memory to store the previous results."
A simple example of a dynamic system is the capacitive system. The capacitor is used to store the charges, so they are also used to store the memory in computers, and the discharging process depends on the number of charges stored an instant before. Therefore, we consider it a dynamic system. More examples are inductive circuits, delay circuits, accumulators, etc.
Have a deep look at these signals. These are the ones that totally depend upon the present and past values of the signal but do not have any concern with the future values.
Keep in mind, that these are not the same as the static or dynamic system, but are slightly different from them.
In non-casual systems, the system depends upon the past, present, and future values, and if any of them is missing, the system is not able to work properly.
We are going to end by discussing the summary of the whole article. We have ready many types of signals and, similarly, systems also have some classification. Most types of systems have an opposite type as well and for convenience, we have discussed them one after the other so that you may compare them and have a clear idea about them. We have discussed some common types of systems and the key points of each type are given below.
System |
Features |
Linear system |
|
Non-linear systems |
|
Continuous system |
|
Discrete system |
|
Invertible system |
|
Non-invertible system |
|
Time variant system |
|
Time-invariant system |
|
Static System |
|
Dynamic System |
|
Casual system |
|
Non-casual system |
|
There are numerous types of systems in which the type of input and the type of output are strongly examined to know the particular type of system. For the best understanding, keep the difference between each of them in mind. There may be other types as well yet for this course, these types are more than enough. You should go through them and find the examples of each of them by summing up your concepts and common sense. You must keep in mind, that a system can be of more than one type at a time. We will go through the next topic in the next step.
Hey peeps welcome to The Engineering Projects. This is the third lecture of this series, and till now, we have discussed the introduction to the signal and system, and in the previous lecture, we learned about the classification of signals and the difference between some of them.
In the present day, you are going to learn the basic operations of signals, and it is amazing to note how you can play with these signals. The best thing about this series is that you are going to see every step with the help of MATLAB. Let’s have a quick glance at today’s topic, and after that, we will go through a detailed explanation.
Addition of Two Signals
Subtraction of Two Signals
Multiplication of Two Signals
Time Scaling (Compression and Expansion)
Time Shifting (Addition and subtraction)
Reversal of Signal
Moreover, you will also learn some practical applications of some of these operations. All these operations are explained with the help of MATLAB code, and for simplicity, the codes are kept basic so that you may learn more about the concepts.
Keep in mind that a signal has some parameters on the basis of which its graphical representation gets a face. These parameters are
Time
Amplitude
In all the operations, we will deal with these two parameters and change their values in different ways. Recall in mind that the greater the amplitude, the longer a signal goes on the y-axis and more time means that we’ll get wider loops of the signals. Time is an independent quantity and it is always kept on the x=axis no matter what type of signals are you dealing with. In each signal, when working on MATLAB, you will put the time in the first place from the left when using the Stem or Plot function.
We are starting with the easiest operation of the wave. The addition of the signal is the process in which the amplitude of two signals is added and as a result, the signal obtain has the combination amplitude of both of these. The simplest example of this operation is:
x1=sin(2πt)
x2=cos(2πt)
y=x1+x2
The resultant Y has the value of the addition of both these signals. Have a look at the same result on MATLAB for the best graphical representation.
Code |
Output |
t=0:0.01:0.1 f=25; t1=2*pi*f*t; x1=sin(t1); subplot(3,1,1) plot(t,x1) title('x1') grid on; x2=cos(t1) subplot(3,1,2) plot(t,x2) title('x2') y=x1+x2 subplot(3,1,3) plot(t,y) title('y= x1+x2') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') |
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Keep in mind, this is not the amplitude at which the operation of addition takes place but the values of the amplitude are summed up and MATLAB store these values and show you another wave of this. You can match the values of the result from the workspace window or simply have a look at the wave. Let’s start from the initial point:
y=x1+x2
At point 0
1=0+1
At point 0.01
1=1+0
At point 0.02
-1=0+(-1)
And so on.
Subtraction is also possible in the signals, just like the addition operation. Subtraction between the two signals takes place when the value of the second signal (the one that is written after the subtraction sign) is subtracted from the first signal.
In MATLAB, for simplicity, we are using the same code with the value of subtraction between x1 and x2.
Code |
Output |
t=0:0.01:0.1 f=25; t1=2*pi*f*t; x1=sin(t1); subplot(3,1,1) plot(t,x1) title('x1') ylabel('Amplitude') grid on; x2=cos(t1) subplot(3,1,2) plot(t,x2) title('x2') ylabel('Amplitude') grid on; y=x1-x2 % Here the subtraction takes place subplot(3,1,3) plot(t,y) title('y= x1-x2') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') grid on; |
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Okay, you must think that this will be the same as the previous two concepts, but no. There is something different from the previous one, but before exploring that, let’s just define the multiplication of the signals:
“The multiplication of two signals is obtained when the values of the amplitude of two signals are multiplied and the resultant signal has the multiplied amplitude.”
Have a look at the MATLAB code.
Code |
Output |
t=0:0.01:0.1 f=25; t1=2*pi*f*t; x1=sin(t1); subplot(3,1,1) stem(t,x1) title('x1') ylabel('Amplitude') grid on; x2=cos(t1) subplot(3,1,2) stem(t,x2) title('x2') ylabel('Amplitude') grid on; y=x1.*x2 % Here the multiplication takes place subplot(3,1,3) stem(t,y) title('y= x1*x2') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') grid on; |
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If you are new to signals and systems, this is something different that you will learn for the first time. At first, you may think that it is a simple multiplication of signals, but soon you will realize that only one signal is used in this operation, the opposite to the case that we have discussed earlier. Have a look at the definition of this operation:
“The term time scaling refers to the process of multiplying a constant by a signal's time axis. This technique is also known as time scaling of the signal."
Depending on the magnitude of the constant or scaling factor, the time scale of a signal has two possibilities:
Compress
Expansion
These two processes occur depending on the amount of time it takes to complete the signal.
Compression of the signal occurs when the constant number, multiplied by the signal is greater than zero and as a result, a signal is obtained that has a less wide form than the parent signal. It is because the time axis has more values in the resultant signal.
You can say it is the opposite phenomenon of the compression of the signal. In this process, the constant number that is multiplied by the signal is less than zero, and therefore, the gained signal has a wider form.
When data is to be brought in at a certain rate and taken out at a different rate, the time scaling operation of signals is a highly helpful tool to have. It will be more clear when you will observe this example:
Changing the rate at which the signal is sampled is the primary focus of the time scaling technique that we employ. Altering the frequency at which a signal is sampled is one technique that is used in the field of voice processing. A system that is based on a time-scaling algorithm that was built to read text to people who are visually impaired is a specific example of this.
This is another operation on the signal in which the x-axis or time axis changes. Instead of changing the width of the signal, we are shifting the wave to a different location on the x-axis.
“The process of moving a signal forward or backward in time is what the term "time shifting" refers to. To do this, either an additional amount of the shift or subtraction from it is applied to the time variable in the function.”
It is interesting that you are moving the whole signal on the time axis. It has two processes:
This process is used to move the whole signal to the right side of the time axis. The whole signal moves towards the right side and the amplitude does not change.
As you can guess, by subtracting the value on the time axis, you can simply move your signals to the left side of the x-axis no matter where they are at the start.
Code |
Output |
t=0:10; x=[0 1 2 1 0 1 2 0 1 2 1 ]; subplot(3,1,1) plot(t,x) title('Simple Signal') xlabel('Time') ylabel('Amplitude') grid on; axis([-2 8 0 4]); subplot(3,1,2) plot(t+2,x) title('Shifting by addition') xlabel('Time') ylabel('Amplitude') grid on; axis([-2 8 0 4]); subplot(3,1,3) plot(t-2,x) title('Shifting by Subtraction') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') grid on; axis([-2 8 0 4]); |
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A significant number of signal-processing applications make use of an operation known as time-shifting, which is an essential procedure. For the purpose of performing autocorrelation, for instance, a version of the signal that has been time-delayed is utilized.
When one is first learning about time scaling, one of the most natural questions to ask is, "What happens when the time variable is multiplied by a negative number?" Time travel is the solution to this conundrum. This procedure inverts the time axis, often known as flipping the signal over so that it reads along the y-axis.
“ The process of flipping the whole signal by using the flipping function or by multiplying the whole signal with a negative number is called reversal of the signal because each and every value of signals is reversed”.
This technique is useful in many cases, and the best thing is, that you do not have to change your code much. Just 1 step and you are good to go.
Code |
Output |
t=0:10; x=[0 1 2 3 4 -5 -6 -7 -8 -9 -10]; subplot(3,1,1) stem(t,x) title('Simple Signal') xlabel('Time') ylabel('Amplitude') grid on; y=fliplr(x); subplot(3,1,3) stem(t,y) title('Shifting by addition') xlabel('Time') ylabel('Amplitude') grid on; |
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There are certain operations on the signals that are too easy to perform but have the ability to change the working of the entire signal. These operations work as the backbone of the signal and system, and once you have command of this, you can work more deeply with the signals. You may also see some other operations in the upcoming tutorial, but for now, you must practice these basic operations and try to make your own signals and play with them. It is an interesting task that must be done on the same day as you learn the basic definition of these signals.
| Where To Buy? | ||||
|---|---|---|---|---|
| No. | Components | Distributor | Link To Buy | |
| 1 | Raspberry Pi 4 | Amazon | Buy Now | |
Thank you for joining us for yet another session of this series on Raspberry Pi programming. In the preceding tutorial, a facial recognition system on a Raspberry Pi 4 was used to develop a smart security system. We also learned how to create a dataset using two Python scripts to train and analyze a series of photographs of a certain person. This tutorial will teach you how to install pi-hole on a Raspberry Pi 4 and use it to block advertisements from anywhere. This is a great initiative for folks who are tired of annoying pop-up adverts while browsing. First, we'll learn how to set up the pi-hole without the need for an environment, then we'll use Docker to install pi-hole, and ultimately we'll see how we can access it from anywhere.
Ads with poor quality are all over the internet, causing havoc with the entire user experience. Various varieties of these intrusive ads are available, ranging from video content that takes control of your browser to ads that infect your computer with malware and steal your private information without your knowledge.
So far, using an ad blocker has shown to be an effective method of preventing advertising of this nature. What if you could have an ad blocker that works on all your local area network devices instead?
Using Pi-hole, an ad-blocking program for the raspberry pi computer, you can block all major advertising networks from loading adverts on your networked devices.
You must first install and configure Pi-hole on your RPi before using it.
DNS server requests are used by all internet services, including adverts, to get you from source to destination. A DNS server translates theengineeringprojects.com into server IP addresses that your web browser can use to connect to the site. As with DNS, ad networks use it to request that their advertising be served.
When you see a Google ad, your internet explorer is likely making requests to domains like theengineeringprojects.com to deliver them appropriately. You have to intercept and prevent these adverts from loading, and that's exactly what Pi-hole does.
You can use Pi-hole to operate as a DNS server for your network. Requests to ad networks are initially routed through Pi-hole, which serves as your Domain name server. Thousands of domains on its blocklist are compared to see if any match these. Ads will be prohibited if the website is blocked, allowing you to have an ad-free experience.
Devices with limited ad-blocking options will find this useful. If you want to avoid adverts on your smart TV or gaming console, you'll need a third-party tool such as Pi-hole to handle the job for you.
Pi-web hole's interface allows you to block or allow specific domains to prohibit strange advertising networks or other questionable sites from loading if you need to tailor the system.
Pi-hole can be installed in two methods on a Raspberry Pi and other Unix distributions such as Debian and Ubuntu. When running a Linux distribution other than rasbian, a single-line command can be used to install it.
Alternatively, you can utilize Docker on the RPi to isolate Pi-hole in a software container. However, Docker requires many configurations, but it does enable you to host pi-hole on a virtual machine.
The fastest approach to get Pi-hole up and running is to utilize the designer's installation script. Running the script via curl or downloading it manually are two options.
Launch a command line and enter:
sudo curl -SSL https://install.pi-hole.net | bash
Before the setup is complete, you can customize Pi settings holes by running the automatic installation script and downloading any necessary packages.
Curling a program from the web is generally terrible practice because you can't preview what the script does before running it, even if it is allowed. You could download your program and then explicitly run it as a last resort.
Obtaining the file is as simple as opening a terminal and typing.
wget -O basic-install.sh https://install.pi-hole.net
sudo bash basic-install.sh
Installing Pi-hole and any other required tools will be completed using the same script used during setup.
Your network connection and chosen logging level will be requested for confirmation at some stage in the installation procedure under the terminal's config choices.
If you don't want to risk losing the randomly created admin passcode displayed at the end of the installation, make a note of that information. If you lose or forget the passcode, you will have to open a command line and run the below to change the password.
sudo pihole -a -p
A Docker container can be used instead of the script supplied above to manage Pi-hole.
Docker is a free software platform for creating containers. With the rise of cloud-native systems, container delivery has gained popularity as a more efficient means of distributing dispersed applications.
It's possible to develop a container without Docker. However, the framework makes the process easier and more secure to do. Docker is a set of tools that make it easy for programmers to create, deploy, operate, upgrade and terminate containers with a single application programming interface and a few basic instructions.
The Unix kernel has inbuilt isolation and virtualization features that make containers practical. Many of the same functionality that a hypervisor provides to allow multiple virtual machines to share a common hardware CPU and memory can also be found in the os.
Since containers provide all the benefits and features of Virtual machines, like software isolation, low-cost scaling, and disposability, they also offer some major new benefits:
Docker provides a shell script that makes it simple to get it up and run.
curl -sSL https://get.docker.com | sh
The following two commands can be used to analyze programs before they are executed:
curl -SSL get.docker.com -o get-docker.sh
sh get-docker.sh
The "permission denied" message will appear if you run several Docker commands, indicating that the root account can only use Docker. For non-root users that want to run Docker commands, the following command will work:
sudo usermod -aG docker pi
It is possible to add users to groups using usermod with -aG. A person called "pi" is now part of a " docker group." This made it possible for pi to perform docker instructions. Any other user can substitute the default pi account.
The command below can be used to confirm this:
groups pi
Check to see if Docker is mentioned as a group.
We will use the hello-world image to see how well Docker works.
docker run hello-world
To tell whether you have installed Docker correctly, you will see "Hello from Docker!"
With the help of Docker-compose, you can create and maintain your environment with YAML files. For applications that require various interconnected services, this is a particularly helpful feature.
To get docker-compose up and running, run pip3 to get it started.
sudo pip3 -v install docker-compose
You'll need to clone the Pi-hole Docker installer from the Pi-hole Git repository to run Pi-hole in a docker container. Let us install Git so that we can get started on this.
Git keeps track of all the modifications you make to scripts, allowing you to roll back to previous versions if necessary. Using Git, many people may merge their contributions into a single source, making it easier for everyone to work together.
You can use Git irrespective of whether or not you develop code that you alone will view or if you are collaborating.
Git program can be executed on a computer's hard drive. You have access to all of your documents and their histories on your computer. Online hosting can also be used to keep a duplicate of the documents and the histories of their modifications. Sharing your modifications and downloading others' updates in a central location makes it easier to collaborate with other programmers. You may even integrate the modifications made by two people working on the same project without losing one another's work, thanks to Git's ability to combine changes automatically.
You may get the software of any os from the Git official site.
Installing Git from the command-line interface is as simple as typing the commands below into your terminal window:
sudo apt-get install git-all
Type in the following command:
git config --global user.name "TheEngineeringProjects"
The quote marks are for your name. The —global parameter specifies that your Git name will be set for all your computer's repositories.
Type the command below to make sure you typed your username accurately when in doubt.
Git config --global user.name
this should return your username:
When pushing code to GitHub, you'll need to provide a valid email address. This can be done in Git.
git config --global user.email "Theengineeringprojects@example.com"
To make sure you've entered your email address correctly, here's a final check:
git config --global user.email Theengineeringprojects@example.com
In a command window, enter the following commands.
git clone https://github.com/pi-hole/docker-pi-hole.git
The pi-hole git repository will be fetched to run Pi-hole in a Virtualized environment. Your container's setup script may be found in the copied Pi-hole directory. You should look over and make any necessary changes to the setup script before executing it.
The program automatically generates an admin passcode for Pi-hole, as are other options like the time - zone Pi-hole utilizes and the standard Domain name server it uses for outbound DNS queries.
./docker_run.sh
Take note of the passcode displayed when the script has been completed successfully. Please note that this passcode is required for further configuration of the Pi-hole.
A reboot of your raspbian should immediately start the service Pi-hole, thanks to its Docker launch script use of the —restart=unless stopped parameter.
However, this only works if you have performed the above steps to activate the container init file to ensure the Docker container is automatically launched upon startup.
Your gadgets should be ready to use Pi-hole now that it has been installed and operating. Default by Pi-hole does not block advertisements in your network. Change your device Domain name server settings to use the Rpi's internet address instead, and they will work.
Each gadget on the local network can be configured for Pi-hole as its Domain name server manually or set up your home network router for Pi-hole instead. To physically configure each device to use Pi-hole, please follow the instructions below.
Your Pi-hole admin interface should begin to show web requests from all devices once configured to utilize the Raspberry Pi's Internet address. Launch an ad-supported application or visit a site like Forbes if you want to ensure Pi-hole is restricting advertisements.
Pi-hole should function properly if the adverts are blocked. In some cases, restarting your devices may be necessary for the Domain name server settings to take effect.
To utilize Pi-hole on many devices within your network, you'll need to configure all of the local network's computers and routers, which is time-consuming and inefficient.
You should use your Rpi's internet address instead of your router's Domain name server settings. As a result, no advertising will be sent to any gadgets on the local area network. By contrast, manually configuring the Domain name server on each device is time-consuming and inconvenient.
To change your Domain name server settings, you will need to know what kind of router you have and what model it is. This information should be displayed on the router or included in the package that came with it.
As a last resort, you might examine your router's guide, use an internet browser, and try out some popular internet protocol addresses.
Internet providers' Domain name servers are typically pre-configured in the router. Ensure the Internet protocol address of the RPi is used as the DNS server.
As a result, all devices connected will be directed to use Pi-hole as the initial gateway for all Domain name server requests. There will be no processing of banned queries, while approved queries will be forwarded to the internet domain name server provider you've selected in your Pi-hole settings.
You may need to reset your router for your new Domain name server configurations to take effect throughout your whole network.
If Pi-hole is up and running, you may log into the administrator site from any internet browser by entering the URL below.
If that doesn't work, it may be necessary to look up your Rpi Pi's internet protocol address if that doesn't work.
Users who haven't logged in to Pi-admin hole's site should be able to see a summary of the service's statistics. Even though Pi-hole is designed to be a "set it and leave it" solution, you will have to make any necessary changes to the settings here.
The Pi-hole administrator site can be accessed by clicking the Login button in the left navigation. Signing in requires you to use the passcode you set up while installing Pi-hole.
If you ever forget the Pi-hole administrative passcode, launch a command prompt or remote SSH connect and use the following command to change the passcode.
sudo pihole -a -p
or
docker exec -it pihole pihole -a -p
When using Docker containers to execute Pi-hole.
You will see all of Pi's features, hole stats, and reports after you have logged in. Pi-hole logs, bans and access control lists, and settings area are all accessible from this left navigation bar.
Most popular advertising networks are blocked by Pi-hole's lists which are frequently updated and managed by individuals and companies.
You can see them by selecting Group Management afterward Adlists in the left menu, where you may deactivate or delete any existing groups, or you can create your own.
Restrict and unblock domains by adding and removing them from the Blacklisted domain list. You can add a DNS server and descriptions to either the Blacklisted or Allowed domains menu by clicking on the Add button.
Select the red delete button symbol next to any entry in the Category of items section below that you want to delete.
If you've got an RPi running Pi-hole, you can utilize it as the Wi-Fi network's domain name server. At home, this is a terrific way to relax. However, you must be at home for this to work. Your Pi-hole must be accessible from any location if you wish to utilize it to prevent advertisements.
Pi-holes in the cloud is the most obvious method of accomplishing this. As long as you don't take further safeguards, malicious actors could exploit your Pi-hole to target other network portions. You also need to subscribe to it and integrate a cloud server. Regardless, we'll go with the low-cost and simple solution of using our RPi with Tailscale.
There is no better way to connect every device safely and conveniently than Tailscale. It gives you the option of selecting a Domain name server.
Tailscale can be used for free in most situations like this by individuals.
the first step is the installation of transport HTTP
sudo apt-get install apt-transport-https
Afterward, include the tailscale sign key and repo in the
curl -fsSL https://pkgs.tailscale.com/stable/raspbian/buster.gpg | sudo apt-key add -
curl -fsSL https://pkgs.tailscale.com/stable/raspbian/buster.list | sudo tee /etc/apt/sources.list.d/tailscale.list
With the code provided below, tailscale is now up and running
sudo apt-get install tailscale
Link your computer to the Tailscale network by authenticating and connecting it there.
sudo tailscale up --accept-dns=false
Pi-upstream hole's servers are Linux-configured Domain name servers, to which it sends DNS requests it cannot answer. Pi-Hole should not attempt to act as its source as it will serve as our Domain name server in this configuration.
Now you're linked up! You can discover your Tailscale Internet protocol address by:
tailscale IP -4
Tailscale's official website has the software you need to get started.
Tailscale's administrator console allows you to set up Domain name servers for your whole network. As a universal name server, provide the Internet address of your RPi's Tailscale as the Domain name server address.
Ensure to use the Override domain Name server option upon entering the Rpi's Tailscale Internet address so that our internet Domain name server will overwrite any local Domain name server settings that endpoints may have.
The security of your network may require that from time to time, you re-authenticate your devices with Tailscale. You'll want to turn off key expiration on the RPi in the administrator dashboard to prevent Domain name server outages when this happens.
That's all there is to it! Whenever you sign in to Tailscale, the Pi-hole will immediately serve as the Domain name server for that machine.
If the Pi-hole is preventing you from accessing whatever you need, you can deactivate it by deactivating Tailscale and reconnecting whenever you're ready.
If something goes wrong, you'll want to be comfortable with the Pi-hole administrator interface, but you won't need to use it regularly. Advertising networks and trackers will be secured and blocked on all or some of your equipment when your gadgets have been configured with Pi-hole in the background.
Because of Docker, you can run multiple programs on the Raspberry Pi simultaneously, providing a 24-hour DNS for you to access. As we've described in earlier chapters, you can use a Rpi network storage or a Rpi VPN to protect your privacy and anonymity online.
A list of well-known ad-serving domains is produced using data obtained from third parties.
Using internet filtering, it is possible to ban adverts in many platforms, such as mobile applications and smart screens.
Your network connection will perform better because advertising is prevented before they load.
Use adblocking software with a VPN service for advertisement blocking and data savings.
You can see the number of ads prevented and a query history on the Graphical interface.
Pi-hole blocks not all advertisements; however, the majority of them are. Pi-hole is a Domain name server with some blocked and allowed features pre-installed. It's not much more than that. Those guidelines determine whether or not a request is granted or refused. To filter advertising that does not use a Domain name server, Pi-hole uses a Domain name server and domain matching. This is a common occurrence in games played on smartphones. Ads are a common feature in many video games. It will not be possible to ban adverts that use the same domains as legitimate traffic. You'll have to put up with the YouTube advertising, even on pi-hole.
With Pi-hole and docker container, we learned how to filter intrusive advertisements from the world wide web. Our datagrams will be accessed more quickly, data loss will be minimized, and cost-effective. Using a raspberry pi 4, we'll develop a voice recognition system in the next chapter.
Hello! Welcome to the engineering projects. This is the second part of the signal and system series in which we will discuss some essential classifications of simple signals. In the previous session, we discussed the introduction of signals and systems and also ran some simple codes on MATLAB for the implementation of some simple codes.
In this session, we are discussing some essential types of signals, and the best part is that we will implement all the signals in MATLAB for the best understanding. Here is a quick glance at all the topics that we will discuss today:
Continuous-Time Signals
Discrete-Time Signals
Periodic Signals
Aperiodic Signals
Even Signals
Odd Signals
Deterministic Signals
Non-Deterministic Signals
Energy Signals
Power Signals
What are functions?
Some examples of signals
Difference between some signals
It is a signal that does not contain any breaks and is referred to as a continuous-time signal.
Differential equations are used to describe this. This signal is represented by the letter x(t). Because of their historical significance, CT signals are frequently referred to as analog signals.
Controlling the speed of a DC motor by the use of a tacho generator's feedback, sine waveforms, or exponential waveforms. The well-known mathematical concepts of differential equations, continuous convolution operators, Laplace transforms, and Fourier transforms are what differentiate linear CT systems from other types.
A signal is said to have a discrete-time signal if its value can be measured at discrete intervals. There will be time intervals of n during which you do not have a value when you are working with a discrete-time signal. The form x[n] is utilized in the representation of DT signals. Continuous-time (CT) signals are approximated by discrete signals.
Difference equations, discrete convolution operators, Z-transforms, and discrete Fourier transforms are some of the mathematical tools that can be used to represent linear DT systems.
Once you have understood these concepts, you must know there are further types of these signals as well. Keep in mind that every signal is continuous or discrete, and these are further divided into sub-types. These sub-types are given next:
A signal is said to be periodic if it satisfies the following equation:
𝑥(𝑛) = 𝑥(𝑛 + 𝑁);
where n is a positive number. In other words, a signal is said to be periodic if it repeats the same sequence of values exactly after a predetermined amount of time, which is referred to as the period.
Sine Wave
Here, we are going to present some lines of code that when entered into the MATLAB window, you will observe a sinusoidal wave.
Code |
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A=7; f=10000; T=1/f; t=0:T/10:5*T; y1=sin(pi*f*t); plot(t,y1) xlabel('Time') ylabel('Amplitude') title('Periodic Signal') grid on |
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As we know, all waves have an amplitude, frequency, and time period. Simple code is explained in our previous lecture, but in this code, you must notice that the amplitude and the whole wave repeat their pattern after a particular time period that is exactly the same as in the previous section.
As you can guess from the name, an aperiodic signal is one that can be represented as
𝑥(𝑛) ≠ 𝑥(𝑛 + 𝑁);
Here, n is a positive number.
The signal does not repeat itself after a particular time interval; instead, it has a different pattern at every point.
As you can see in the output, the wave’s pattern is not predictable. You can do the same thing by using a “Random” function that you will see in this same article in just a bit. For now, there is no need to understand all this code, you just have to observe the pattern in the output.
The term "even signal" or "even function" refers to a signal that is symmetrical at the time origin or the vertical axis, respectively. The even signals are also referred to as symmetrical signals for this reason.
Mathematically,
x(-n)=x(n)
In other words, the values on the right-hand side are exactly symmetric to the left-hand side of the axis.
Cosine Wave
A signal is referred to as "odd" if it is anti-symmetrical on the vertical axis. An odd function is another name for an unusual signal. As a result, the signals that are odd are sometimes referred to as antisymmetric signals.
Sine Wave
Code |
Output |
n=-2:12 x=sin(4*pi*n/5) subplot(2,2,1) plot(n,x) title('Odd Signal') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') grid on; xo=-sin(4*pi*n/5) subplot(2,2,2) plot(n,xo) title('Odd Signal') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') grid on; |
Here, in the output, you can see two signals. When we replace the equation with the negative sign, we find that it is flipped and is non-identicle to the first picture. Hence, it is an odd signal.
When there is no room for interpretation regarding a signal's value at any given moment in time, we say that the signal is deterministic. Or, signals are referred to as deterministic when they are capable of being characterized in an accurate manner by a mathematical formula.
Let’s say we have a formula that shows an equation or a signal, then we can predict the result or the graphical representation with the help of that formula, and such signals are referred to as deterministic signals.
sine wave, square wave.
Code |
Output |
n=-2:10 x=sin(4*n/5) subplot(2,2,1) plot(n,x) title('Deterministric Signal') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') grid on; |
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These are contrary to the one that was discussed before. The result of such signals is not predictable, and therefore, a formula can not be set to represent non-deterministic signals. In one case, they are shown with a certain value, and in the next case, the values change abruptly. Because of the nature of providing random values with these signals, they are also called random signals.
Noise in communication is an example of random signals because no one can exactly predict the noise value during communication.
Code |
Output |
x=rand(1,100); plot(x) title('Random Signal') xlabel('Time/ The Engineering Projects') ylabel('Amplitude') grid on; |
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Here is an interesting example for beginners. Basically, this code comprises two steps that are used in the functionality of the signal. We have used a function called “Random” and represented as rand(a,b) where a and b are the peak values in between which, this function displays any number randomly without any pattern. In the next step, we will just plot the signal and got the perfect example for the random function.
Energy signals are the ones that contain a finite amount of energy in them. The energy of such signals can be calculated using different techniques, but the power of such signals is infinite. Mathematically,
0 < 𝐸 < ∞
Aperiodic signals
In contrast to energy signals, power signals have a finite power that can be observed and measured, and the energy of these signals is infinite. By using mathematical representation, we can say,
0 < 𝑃 < ∞
Periodic signals
Just like any other programming language, MATLAB also has some pre-defined functions and in this course, we will use some of these according to the need of time. You have observed that some functions are also present in the codes that we have discussed today and now, we are going to discuss some explanations about these functions so that you may have an idea about the working and needs of these functions.
We can write a function independently from the main program, without having to consider how it will interact with the rest of the program as we do so. A function can be thought of as a miniature version of the main program. Because of this, we are able to break down a large program into smaller, more manageable portions, which ultimately results in a reduction in the total complexity of our program.
Flip is an interesting function in MATLAB that can be used to flip the whole signal in just one step. There is no need to write the code with different signs and information. Mathematically, the flip function is given as
B = flip( A, dim )
Where
B= Any variable that is used to store the result of the flip function so that you can take further steps.
A= The signal that is to be flipped. You can also give the signal to any name.
Dim= dimensions at which you want to flip your signal.
We have used this function in our code where we had to find that is our signal even or odd. It is just an example. This function is also used in other codes according to the needs of the programmer.
Random Function is used to have a uniformly distributed random number that is set by the programmer according to need. There are different forms of random functions that are used in random functions and some of them are:
Y = rand(n)
Y = rand(m,n)
Y = rand([m n])
Y = rand(m,n,p,...)
Y = rand([m n p...])
Y = rand(size(A))
Out of which we have used the second one, where we have given the two dimensions to the random function. This returned us an m-by-n matrix of random entries, and we used it for our aperiodic signals.
In the case given above, the result of this random function is stored in the Y variable so that it can be used again for more actions.
While using these signals in our codes, one must be clear about the difference between some same kinds of signals and it is a good practice to have to keep them in mind in the form of points so that you may have the idea about the best use of these signals. Here are some important points to keep in mind.
Continuous-Time Signals |
Discrete-Time Signals |
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Periodic Signal |
Aperiodic Signal |
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Even Signal |
Odd Signal |
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Deterministitric Signals |
Non-Deterministitric Signals |
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Energy Signal |
Power Signal |
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Signals have a different type but all of these can be represented as discrete or continuous. We use these types many times while we are dealing with the signal and system and it is important to have the idea of pre-defined functions so that we may minimize the code size with fewer errors.
Signal and systems is an essential subject in electrical engineering and it is not just limited to this particular branch of engineering but students of many other branches such as computer engineering learn and practice this subject in their field. For design and analysis, all engineering topics make use of models of real-world things. Signals and systems provide you with the ability to take on the challenge of getting the job done.
Signal and system are two terms that, when studied and performed together, form a fantastic visualization of different phenomena. Have a look at these two terms.
A signal is defined as the description of comparing two parameters and how they vary with each other. Signals are the representation of some sort of information with the help of some visual aid. Signals are usually categorized into two types:
Analog signals
Digital signals
We’ll go through the introduction of both of these one after the other.
Analog signals are the types of signals that change continuously without any breaks. These signals describe the quantities that have varying values at every point. Therefore, as these signals vary according to time, they are defined over continuous independent variables. Because analog signals have a large amount of information in them, they are comparatively difficult to analyze. At the same time, these signals provide accurate information because the information of every point is stored in them.
Keep in mind, that these infinitely varying signals require infinite memory to store the information of every point on the real line. A sine wave is used to present the analog signal. For a better understanding, we must go through the example of an analog signal.
One of the most understandable examples of analog signals is speech. When humans (or any other animals) speak, there is the formation of continuous waves in the air due to the pressure we exert on the air through our throats. We all know that pressure is an analog quantity and is the mathematical operation with the independent variable of space and time. Other examples of analog signals are:
Time
Temperature
Distance
Sound
The word "digital" means discrete, and therefore, digital signals are defined as discontinuous signals. These are less accurate signals because they do not have all the information stored continuously in them. In digital signals, there are only two variables on which the whole system depends. These are 0 and 1. In return, the results are then also represented in the form of these two variables. These are easy to analyze and require a finite amount of memory to store the information.
The Digital Watch is one of the easiest examples through which you can understand the concept of a digital signal. We can have the values of the hours, minutes, and seconds but not have the values in between the seconds. Keep in mind, that there is an infinite number of values even between the seconds that can not be accurately obtained with the help of the digital system.
Any physical collection of components that can both receive and produce a signal is referred to as a system. When speaking in terms of engineering, the input is typically some type of electrical signal X, and the output is typically another electrical signal (the response). Example of System
A system is anything that contains the components that act on the input signal, and after the procedures, the output is obtained on the other end. For example, a system of different procedures is made to remove the noise from the voice. At end A, the voice with the noise is fed into the system, different procedures occur on it and at end B, a pure voice is obtained without noise.
Another example is the system of images in which the pixels of the images are sharpened by using different techniques, and at the output, we get a sharpened image. Other examples of systems are given as:
A communication system is a system that outlines the process of exchanging information between two different locations.
A control system is a system that governs the output to achieve the appropriate reaction. Control systems can also be referred to as command and control systems.
The auditory system in the central nervous system is responsible for converting a diverse range of relatively modest mechanical impulses into a convoluted series of electrical signals.
The concepts of analog and digital signal processing, which are at the core of contemporary communication and measurement, are discussed in Signals and Systems. In this section, we will discuss the fundamental ideas behind signals with continuous-time and discrete-time in the time and frequency domains. The Fourier transform establishes a connection between time and frequency.
If all of these are confusing at the moment, then do not worry, because we are going to discuss all the concepts used in signals and systems in detail without skipping any points. The good thing is that we’ll be using practical techniques to implement the rules of this subject in different engineering software, mainly MATLAB.
We have read about the types of signals, but here, it is important to discover some important differences between these two types of signals so that you may choose the best one for your experimentation according to the requirements.
Element |
Analog |
Digital |
Representation |
Continuous |
Discontinuous |
Analysis |
Difficult |
Easy |
Accuracy |
More Accurate |
Less accurate |
Type of memory |
Infinite |
Finite |
Digits for representation |
Infinite |
0,1 |
Example |
Human Voice, Pressure, Analog Clock |
Digital watches, Digital phones, Digital pens |
MATLAB is a complex calculation software used in many branches of science, especially in the field of engineering, for many purposes. It is made by a company named Mathworks and has fantastic functions and usage that provide a powerful practice medium for engineers. It has numerous applications and is divided into different sections that can be programmed. Basically, MATLAB is a programming language, and for this course, you just have to keep in mind that we’ll define the signals, build the system, provide all the given information, and use different functions on signals to obtain the required results.
We’ll use MATLAB R2016a in this series.
This is a high-level matrix and array language that supports
Object-oriented programming
Flow control statements
Functions
Data structures
Input/output
and many other languages. It enables "programming in the tiny," which allows for the rapid creation of quick throwaway programs, as well as "programming in the huge," which enables the creation of complete large and complicated application applications.
Basic knowledge of computer programming.
Basic concepts of variables, constants, expressions, statements, and some others.
Mathworks free account.
Operating System |
Windows 10,11, Window Server 2019 |
Processor Requirement (Minimum) |
Any Intel or AMD x86-64 processor |
RAM (Minimum) |
4 GB (8 GB is recommended). |
3.6 GB ( MATLAB) 5-8 GB (Typical installation) 31.5 GB (product installation) An SSD (Strongly recommended) |
Creating a Mathworks account is super easy. You just have to provide and confirm your email address and set the password.
If you are a beginner at MATLAB, then you must know the components of the main screen of MATLAB and the workings of each window. Let’s have a picture of the screen of MATLAB, and all the things will be clear to you in just a bit.
The command window, which also goes by the name main window, has the job of carrying out the instructions that users type into it.
This is the list of folders that are present in your computer’s specific folders, and for our tutorial, you do not have to know much about it at this stage.
You can pick one of the different functions from this menu, and in this tutorial, you are going to choose the Live Script for the easiest functioning from the drop-down menu.
When variables are initiated in the code, the values of each of them are shown in this window.
This sign indicates the line of the code where you are writing at every step.
Here, we are discussing some important and simple commands that may or may not be used in every code according to the voice of the user. But for professional users, it is a good practice to use them as they make the result clear.
This command creates a grid in the resulting window so that you may have the best idea of the scale of your restaurant signal.
As the name specifies, this creates a title for the result and you have to write the string (which you want in the place of the title) in the single comma notation close to the parentheses just after writing this command.
Just like the title, you have to write the string that should appear on the x-axis of your singal by using this command.
This command is used to provide a string message on the y-axis.
Here comes the exciting part. We are going to make simple signals in MATLAB so that all the concepts given above will be clear at once.
Start your MATLAB software.
For best results, it is convenient to work on the live script because, in this way, you are going to check the code at every step and examine the result in the same window.
Write the code given below on the command window:
A=5;
f=5000;
T=1/f;
t=0:T/100:5*T;
y1=sin(2*pi*f*t);
plot(t,y1)
xlabel('Time')
ylabel('Amplitude')
title('Continuous Time Sine Wave')
grid on
We have specified the variables A, f, T,t,y1, and the details of each of them is:
A= Amplitude of the sin wave
f=frequency of the wave
T= Specifying that period is inverse of frequency
t = the time of starting, number of steps, and ending of the wave.
y1 = name of the wave in which we have given the formula of the wave that we want to display.
By using all these variables and formulas, we told MATLAB that we wanted a wave of this size to have this specific type of wave.
The plot is the function of plotting the continuous waves. We have specified that we want a wave by using the time on the x-axis and the y1 formula of the wave on the y-axis. In general, the formula is plot(x,y).
Right now, just copy and paste this code into your live script and observe the results.
x=[1 2 3 4 5 6 7 8];
n=[0 1 2 3 4 5 6 7];
stem(n,x)
xlabel('Time')
ylabel('Amplitude')
title('Discrete Time Wave')
grid on
As mentioned for the analog signals, we have just made two types of waves, where x is the value of the wave at the x-axis and n is the value of the wave at the y-axis. At every step, we have used the function of stem and specified the values where
stem(x,y)
The number of values on the x-axis must be equal to the number of components on the y-axis.
Analog does not equal continuous, and digital does not equal discrete. On the other hand, in popular usage in the context of digital signal processing, analog systems are typically continuous in time and value, whereas digital systems are typically discrete in both time and value. Therefore, there is some improper use of the language.
You can use a multimeter to figure out what's wrong with the electrical system in your car. Most of the time, if you check for voltage and continuity, you can figure out where the problem is coming from. This article will show you how to use a multimeter on a car.
First, make sure the multimeter isn't on. Then connect the positive lead to the positive terminal on the battery. Connect the negative lead to a metal piece on the frame of the car. The last step is to turn on the multimeter and read the results. If it says 0 volts, it means that no electricity is moving through the circuit. If the voltage is 12 volts or more, then there is a current in the circuit.
A multimeter can be helpful if you can't figure out what's wrong with your car's electrics. You should be able to fix many common electrical problems on your own if you check for voltage and continuity.
A multimeter can help you figure out what's wrong with your car's electrical system if it's giving you trouble. A multimeter is a tool that measures the voltage, current, and resistance of an electrical circuit. You can find out what's wrong with your car's electrical system by testing different parts of it.
If you're like most people, you probably don't think about your car battery until it's too late. When this occurs, you know something must be changed. However, replacing a car battery is expensive, and you can avoid having to do so by testing it frequently.
The best tool for testing a car battery is a multimeter. Checking your car's battery with a multimeter is simple. It is simple to use, It can save you a lot of money in the long run.
1. Set the multimeter to "DC Volts" mode.
2. Connect the multimeter's positive lead to the positive terminal of the car battery.
3. Connect the multimeter's negative lead to the negative terminal of the car battery.
4. Measure with the multimeter. If the reading is 12 volts or higher, your car battery is in good working order. If it is less than 12 volts, it is time to replace it.
5. Turn off the multimeter and disconnect the leads from the terminals.
Testing your car battery regularly can help it last longer and save you money on future repairs. Don't wait until your battery is completely depleted to see how well it works. Pick up a multimeter and experiment with it today.
A car's headlights are an important safety feature. As a result, it is essential to make sure that they are in good condition. A multimeter is a tool you can use to check the condition of your headlights.
First, you must locate the ground wire. This is typically one of two or three wires that connect the connector to the headlight. The ground wire is whichever wire is connected to the chassis. Once you've located the ground wire, switch your multimeter to the resistance setting to test it.
Connect one probe of the multimeter to the ground wire and the other probe to the negative end of the car's battery to accomplish this. If the link between these two points is broken, the ground wire has been severed and must be replaced. Check your headlights frequently to ensure they are still working properly and keeping you safe on the road.
There are two ways to use a digital multimeter to find out if a fuse has blown. First, Set the multimeter to the continuity mode and connect the leads to both sides of the fuse. If the fuse works, the multimeter will make a sound. If the fuse is burned out, the beep won't work.
The second way to use a digital multimeter to find out if a fuse is blown is to use the Ohm setting. To do this, set the multimeter to the Ohm setting and touch one lead to one side of the fuse and the other lead to the other side of the fuse. If the fuse is good, the multimeter will show a low resistance. If the fuse is blown, the multimeter will show a high resistance.
You can also use an analog multimeter to check if a fuse is blown, but it is not as accurate as a digital multimeter. To use an analog multimeter, you would set it to the continuity setting and touch one lead to one side of the fuse and the other lead to the other side of the fuse. If there is continuity, the needle on the multimeter will move. The needle won't move if nothing stays the same.
Using a multimeter to check if a fuse is blown is a quick and easy way to find out if the fuse needs to be taken out of its housing. This can be helpful if you can't get to the back of the fuse panel or don't know which fuse controls which circuit. Always be careful when working with electrical circuits, and make sure the power to the circuit is turned off before you use a multimeter to test it.
A multimeter is a tool that every car owner and mechanic needs. You can use it to test a car's charging system, voltage, and current. By using a multimeter on a car's alternator, you can make sure it's working right and avoid problems down the road.
1. Make sure the multimeter is turned OFF.
2. Set the multimeter to the "DC volts" setting.
3. Connect the black multimeter lead to the alternator's negative (-) terminal.
4. Connect the red multimeter lead to the alternator's positive (+) terminal.
5. Switch on the multimeter and take a reading.
6. Compare the reading to the voltage listed on the alternator's label.
7. If the reading is less than what is specified on the label, the alternator may be faulty.
8. If the reading is higher than the label value, there could be a problem with the battery or charging system.
You can ensure that a car's alternator is working properly by testing the voltage and current with a multimeter. This can help you avoid problems in the future.
To find out how much electricity a car battery generates, set the multimeter to "20 volts." This is the most commonly used voltage measurement setting in cars. Analyze the user manual that came with your multimeter.
There are a few ways to use a multimeter to find a short circuit in your car. One way is to test the circuit to see how well it works. To do this, disconnect the positive wire from the battery and put the positive probe of the multimeter on the load side of the fuse. The negative probe needs to be put on the battery's negative end. If there is a short circuit, the test light will turn on or the multimeter will beep.
A multimeter can also be used to find a short circuit by measuring the voltage drop across the circuit. Connect the positive probe of the multimeter to one end of the circuit and the negative probe to the other end. If the voltage drops a lot, it means that there is a short circuit somewhere in the circuit.
If you think there's a short circuit but aren't sure where it is, you can use the process of elimination to narrow down the location. To do this, you'll have to take out each part of the circuit one at a time and check to see if the circuit still works. When the continuity test fails, the short circuit will be caused by the part that failed the test.
When you find the part that is causing the short circuit, you can either replace it or fix it, depending on what you need to do.
Yes, testing a car battery with a multimeter is straightforward. This is a quick and simple test to see if your battery is functioning properly. Simply select the proper setting on the multimeter, then attach the probes to the correct battery terminals. Battery health is good if the reading is within the normal range. If not, a replacement might be necessary.
Multimeters are electrical test tools that are used to measure voltage, current, and resistance. You can use them to check your car's battery, fuse, wiring, and other components. Multimeters can be purchased from most online stores, such as Kaiweets , but before using one, read the instructions. When testing for voltage, always connect the multimeter's red lead to the component's positive terminal. The black wire should be connected to the negative terminal. When testing for current, always connect the multimeter's black lead to the component's negative terminal. The red lead should be connected to the positive terminal. When testing resistance, always connect the multimeter's red lead to one end of the resistor being tested. The other end of the resistor should be connected to the black lead. Always disconnect the multimeter's leads from the thing you're testing before taking any measurements.
Several manufacturing processes for plastic manufacturers and metalworkers, like milling or casting, produce burrs. However, to guarantee the safety and quality of a component, one needs to ensure smooth edges that will not cause any problems in further processing or use of the item. Deburring and brushing machines are solutions to this issue.
High-quality deburring technology from Germany can be integrated into casting and cutting machines, and to automatically produce flawless components.
Burrs are unwanted protrusions of a material like metal or resin that can develop during processing.
When picturing a component like a gear, it is easy to understand, that any kind of imperfection can cause serious problems for the machine the gear is used for. Here, we need to make sure it can rotate easily and will not grate and damage other machine parts.
For the safety of other products, assembly processes, and operators, we need to eliminate these imperfections and protrusions.
There are several materials and processes that can cause burrs to appear. This mostly applies to steel producers and metalworkers , as well as plastic manufacturers.
Burrs develop during:
Super Finishing,
Honing,
Grinding,
Broaching,
Milling,
Turning,
Boring,
Drilling,
Metal Sawing,
Pressing,
File Finishing,
Forging,
Casting,
Welding, and
Fusing.
For materials like:
Stainless Steel,
Steel,
Special Alloys,
Copper,
Brass,
Aluminum,
Sinter Metals, and
Synthetic Materials, like Plastic and Resin.
Multiple machines can help remove burrs; from small manual applications for low quantities to fully automated AI-driven deburring machines integrated into serial production.
The German-based company Loeser has used its over 80 years of experience to become the standard for automated deburring with over 500 installations worldwide. Their top-of-the-line automated deburring centers can be linked to computer-controlled wheel handling conveyors to enable a 20 % production increase.
Deburring machines can use several methods to create flawless components. Typically, the process has two to three steps:
Removing the Primary Burrs – This removes the protrusions that have been created during processing, for example with grinding.
Removing the Secondary Burrs – The grinding process can create secondary burs. With scotch brushes and abrasive brushing techniques, the workpiece’s original geometry can be restored, this time burr-free.
Rounding of Edges – This step is optional. The component now no longer has burrs, but still has sharp edges. If required, to reduce the risk of injury when handling the parts, a deburring machine can also round any edges.
There are different kinds of deburring machines and techniques. In general, the machine must be tailored to the individual industry processes and resulting items. Some types of component shapes and materials are better off with a specific deburring method than others.
A professional manufacturer of deburring machines like Loeser will help their clients find the ideal solution for their needs.
Deburring can be achieved via:
Manual deburring machines are small hand tools with curved or hooked sharp edges you can use to cut away burrs.
For punch deburring, you use a punch machine with a mold fitted to cut away the burrs of the created component. This technique is more efficient than manual deburring but does not allow complex shapes.
With the tumbling technique, parts are put in a rotating barrel along with water, compounding agents, and an abrasive media. Burrs get removed with the friction. The result is very fast and cost-efficient, but not very precise.
Like the tumbling technique, here, the components are subjected to a rotating wheel made from abrasive materials that remove protrusions on contact.
In thermal deburring, the burrs are removed by igniting a mixture of gas surrounding the components in a deburring chamber. This process is very fast but requires further processing such as surface treatments like pickling. Here, we also need to pay special attention to the correct mixture of the used gasses.
In electrochemical deburring, the deburring tool is an anodic metal dissolution with cathodes that dissolves the burrs. This technique is typically used to deburr hard-to-reach and very small areas.
During the hole deburring method, a spring-loaded cutting tool removes the burrs that have developed inside a hole, like the inside of a pipe. The component must be positioned very precisely for the cutting tool to go through the hole smoothly.
Brush deburring is a very cost-effective and fast method that can be used on complex shapes. Here, the components are deburred with brush tools, which may contain abrasive substances. Similar to using sandpaper manually, the machines can fit themselves into several shapes and create smooth and rounded edges. This is the most used technique for automated burring machines integrated into processing lines.
Deburring is a necessary process to remove unwanted accumulations of metal or other materials that can develop during various processing methods. Deburring machines remove the protrusions to guarantee safe handling and further processing of the components.
Automated deburring machines with brushes can be used to gain smooth-finished pieces right from the processing line. The German company Loeser has established itself as the leading manufacturer of efficient deburring processes, which can raise productivity by as much as 20 %.
Electrical equipment has the potential to be extremely hazardous and every year in the US 30,000 incidents of electric shock are reported. As well as causing burns and serious injury to the body, electric shocks can be life-threatening, while the electrical fires caused by damaged wires or malfunctioning equipment can also destroy buildings. When you are working on an electrical engineering project, it is essential to meet electrical safety standards and follow regulations in order to keep people and buildings from harm. Just as you need cybersecurity to protect ideas and abstract designs, regularly monitoring, inspecting and managing any practical electrical work with regular risk assessments will ensure that any system is safe to install and operate.
If you become responsible for an established electrical system, it is important to regularly look out for damaged or exposed wires. Although they are sometimes difficult to spot, if left undetected bare wires can be extremely hazardous causing electrocution or electrical fires in a property. Cables may be frayed over time due to wear and tear but wires may also be exposed by rodents such as squirrels and mice that chew through the insulating sheath. Once damaged wires are found, immediately turning off the electrical circuit will ensure no electricity is running through them. As any contact with exposed live wires can cause an electric shock, this will remove the potential for injury or electrocution . As a temporary measure, superficially damaged wires can then be repaired with electrical tape but, in the longer term, exposed wires should be completely taken out and replaced.
As well as regularly inspecting established power systems, as an electrical engineer you may be responsible for designing a new electrical distribution system in a building. By familiarizing yourself with the National Electrical Code or any other regulations that apply where you are working, you can ensure that fundamental safety principles are established and that your design will be reliable and safe. A good electrical system design should be able to cope with the normal everyday requirements of the building together with occasional peaks in demand. However, all systems must include a circuit-protection strategy that will usually include fuses, relays and circuit breakers. This will disconnect the electricity supply by interrupting the flow when an abnormal or dangerous load is present.
When a circuit breaker is tripped it could be the sign of an electrical circuit overload. In a home or office, too many appliances plugged into one outlet can exceed the load for the circuit wiring which will cause the breaker to trip and shut off the power. While tripping the circuit breaker is an effective safety measure, it causes disruption to the electricity supply and should still be avoided if possible. Some of the signs of potential overloading before the circuit breaker is tripped include switches that are hot to the touch, outlets that produce a burning odor or plugs that have been scorched around the edges. By mapping circuit layouts, it is possible to calculate a safe load rating for each circuit . If the demand of a building outstrips the safe supply of electricity, you may need to install a new circuit layout to take the additional load.
A successful electrical engineering project goes beyond good design, it must also be safe to install, operate and use on a day-to-day basis. By following electrical codes, carefully monitoring systems and carrying out regular risk assessments, any potential hazards can be removed and the safety of engineers, operators and end users is assured.