hello and welcome back to this channel this is Professor a book author of 25 Plus Engineering books Dear students this is the first session for the subject signals and systems I will explain you the different types of signals this topic is required is it is very much important because we'll be using these words these types of signals throughout this subject so first of all the definition of term signal signal is a physical quantity that varies with one or more variables in our daily life also we use this term signal anywhere for example we say traffic
light signal then satellite signal TV signal mobile signal then while performing practicals we use this type of signals like sine level signal then triangular wave signal Square wave signal and so on so signal is a general word under signal there are different types first type is continuous or discrete signal a continuous signal is also abbreviated as CT it is also known as continuous time signal or discrete time signal which is abbreviated as a d t discrete time signal next is periodic or non periodic signal if signal is repeating it is periodic otherwise it is non
periodic next is even it is also called as symmetric or odd which is also known as anti-symmetric or asymmetric signal next is fourth is energy or power signal and last type is deterministic or random signal we'll discuss each type in detail the first type of signal is continuous or discrete signal as I mentioned earlier continuous signal is also abbreviated as CT continuous time discrete signal is abbreviated as DT discrete time signal now consider an example of a standard sine wave we know that this is the diagram of sine wave ideally it starts from origin and
the signal repeats up to Infinity the mathematical notation is X of T this is known as a continuous signal or CT signal continuous time signal I have written its definition it is the signal which is defined and represented at any instant of time it is also known as analog signal it is defined as well as represented at any instant of time so at any instant some amplitude is present it might be zero and at other instance it is again changing so it is continuously changing with respect to time period it is known as continuous time
signal it is also called analog signal next is the diagram for discrete signal now before that the mathematical notation is X opting this x when I write X of T we know that t represents the time period we read it like this x is function of time period x represents amplitude of signal so X is amplitude T is the time period mathematically if we read it like this x is function of time period that means amplitude is function of time period or amplitude is changing with respect to time period this x also represents the shape
of signal so the notation is X of t x is amplitude T is the time period now mathematical equation of this continuous type signal I mean for this sine view we know that it is represented like this a sine Omega t a is maximum amplitude sine y I have written sine because the nature of wave is sinusoidal if it would have been a cosine view I would have written a COS Omega T Omega is angular frequency which is 2 pi f t is the time period this is the mathematical formula for the side wave signal
which I have drawn it is known as the CT signal or continuous time signal which is function of time period that means it is changing with respect to time period it is also called analog signal next is the diagram for discrete signal make the thing simple if the signal is in the form of pulses it is known as a discrete signal how to write a definition of this we have discussed the definition of CT signal just make few changes the original statement remains same it is the signal which is defined and represented at instead of
any instant of time we will have to write at certain instant of time look at this diagram I have written on x axis I have written some variable n this n is known as index it represents a corresponding number whatever things I have drawn each thing is called as a pulse so n is index which represents presence of pulse value of n which is value of index is always at an integer like 0 1 2 3 4 up to Infinity it cannot be a non-integer value so it is the graph of x open versus set
what is the change in the first diagram in case of CT signal on x axis I have plotted T that is time period in case of DT signal I have to plot n which is representing an index and draw the diagram in the form of pulses so this pulse indicates presence of signal for example if this amplitude is 0 I have marked here 0 suppose I will Mark some instance like like this suppose at this instant amplitude is one hold at second instant amplitude is to hold at third instant amplitude is again one volt and
so on again at this instant it becomes zero so what I have done at 0 I have marked the point of zero at this value of time period say it is one second as an example then at one second amplitude is one whole so I have drawn a pulse representing one hold at say two seconds this is the time instant representing two seconds at two seconds amplitude is too old what I've done I have marked a pulse of the amplitude of to hold then at let us say this is three second at three second again
amplitude is one whole marketer pulse likewise go on marking different pulses whatever signal you are getting that is known as DT signal that is discrete time signal the specialty of this signal is if you join all these pulses like this again we are going to get the same signal which is the original analog signal so this is known as a discrete time signal or DT signal keep in mind in case of T I have used the notation n what about the mathematical expression as I said if you join these pulses again you are going to
get the original signal original signal is a sine wave this is again a sine wow but it is in the sampled form which is known as a discrete form now how to write the mathematical equation through the subject there are two types of equations one is continuous another is distribute order to mug up the things I will tell you simple trick if you know the equation of continuous time signal just replace T by n for example I have already discussed this equation of a sine wave which is a sine Omega T if I want to
write mathematical expression for discrete sine view for this diagram then how to do it keep a as it is keep sign as it is because it is again a sinusoidal signal but it is in discrete form Omega is again as it is only in place of T I will have to write n so X of N is a sine Omega n that's it this is the mathematical expression for discrete time signal so it is the signal which is present only at certain instant of time this certain instance are known as discrete instance or discrete type
you can well Define it as it is the signal which is present at some discrete time instance and that is the discrete time signal then the question arises whether this DT signal is a digital signal a signal which is discrete in amplitude as well as time I am repeating a signal which is discrete in amplitude as well as time is known as a digital signal whereas this exotic continuous signal is known as the uh analog signal so these are the basic types what is CT and another rigidity signal related to this or rather extension of
this is the next type that is periodic or non periodic signal as the name itself indicates periodic means the signal should repeat after some time period for example I have drawn this sine wave as I mentioned earlier this is the sandwich which is ideally till Infinity like this it goes on increasing till Infinity I will Mark Few readings we know that this is zero origin this is pi this is 2 pi from 0 to Pi there is a positive half cycle from PI to 2 pi there is a negative half cycle after 2 pi again
the signal repeats like this so This same portion is getting refitted till Infinity this is known as a periodic signal very simple so if the signal repeats itself after certain time period in this case this time period is 2 pi so after 2 pi in the present case the signal repeats itself it is known as a periodic signal now after which value this signal repeats it is getting repeated after the value 2 pi so this value 2 pi is known as fundamental period so in this case the value of fundamental period is 2 pi because
after 2 pi signal repeats very simple the value after which signal repeats is known as the fundamental period notation is capital T So capital t is equals to 2 pi again through this subject there are many notations but you have to remember it logically make the thing simple it is CT signal that is continuous time signal which is represented by X of T small T is the basic notation in case of periodic signal the period after which signal repeats is denoted by capital T since there is a small time using notation capital T So capital
t is equals to 2 pi what about units this is actually value of time period but it is in terms of Pi so unit is a Radiance if it would have been only 2 3 like this I would have written the unit seconds presently it is 2 pi radians now mathematically any periodic signal can be represented like this x of T is equals to X of t plus capital T very simple after capital T that means after 2 pi value of capital t is two point in this case the signal repeats so X of T
is same as X of t plus capital T or after capital T I mean after this value which is 2 pi which represents capital T same signal repeats so mathematical equation is X of T is equal to X of t plus capital T now this is the discrete signal which is obtained from The Continuous signal just now I explained if you join all these pulses you will get the original signal back so it is similar to The Continuous signal only nature is discrete so it is known as a discrete type signal now how to write
mathematical Expressions again on the same lines you will have to just make changes in the notation for example this is the equation x of T is equals to X of t plus capital t is the mathematical equation of periodic signal for c t that is continuous time signal if I want to write mathematical condition for DT signal then making use of this same equation I can write it like this x of n is equals to X of n plus capital N very simple in place of small T I have used small n in place of
capital T I have used notation capital N so if this condition is satisfied then discrete signal is periodic in nature now in this case what I said capital t is equals to 2 pi that means after 2 pi values repeat signal repeats in this case I have written few numbers like 0 1 2 3 you can well say after value 8 when n is equals to 8 you are getting 0 as like the original case again after it you are going to get the same diagram like this so 8 is the value after which signal
repeats so fundamental period for discrete signal in this case is n is equals to n what about unit in the earlier case it was 2 pi so we said unit is Radiance in this case n is equals to 8 what this number 8 indicates it represents number of samples we will refer it like this this is zeroth sample first sample second sample likewise eighth sample so after eight values are repeating so n is equals to A N is fundamental period which is 8 and unit is samples so it is repeating after eight samples so these
are very important types one is CT and DT and next is periodic or or non-periodic signal the next type of signal is even or order signal I have drawn four diagrams two four continuous signal and remaining two for discrete signals let us talk about this first diagram just now we discussed when I write X of t t represents time period x represents amplitude I have drawn one signal uh Hub part of this signal is at positive time period remaining half portion is at negative time period suppose I will Mark Few notations if I will say
this part which is present on positive time period is a whereas part of this signal present at negative time period is B we can easily say the two parts A and B are equal having same area and they are symmetric about vertical axis so when the signal is symmetric about this is the vertical axis when the signal is symmetric about vertical axis it is known as symmetric signal or even signal another name of human signal is a symmetric signal now how to write the mathematical equation again you don't have to bug up the things I
will tell you simple trick how to generate mathematical equation just now we discussed one concept when we write X of t t represents time period x represents amplitude of signal if I want to write mathematical expression for part A just you have to think for part A amplitude is positive see any amplitude which is above this line This is the horizontal line This is the zero value any amplitude which is above this line is positive if amplitude would have been below this line it would have been negative so amplitude of party is negative amplitude is
not denoted by X time period for part A this is at rhs of time axis so time period for part A is again positive so mathematical expression for part A can be written as plus X of plus t y plus X as I mentioned amplitude is positive so X represents amplitude so it is plus X time period is also positive for part A so it is plus T Simply It is written as X of T now Part B as we discussed part n Part B are symmetric they are same having same area for Part B
amplitude is positive amplitude is the portion it is the portion which is about the zero line about this horizontal line so amplitude is positive so for amplitude I will write plus X but for Part B type where it is negative because part B is at left hand side of this axis so any time period which is at LHS of this line is negative time period so since the time period is negative I will write minus t so mathematical equation for Part B is plus X of minus t or simply X of minus t plus is
a material so it is X of minus t that means we can well say like this if the mathematical condition X of T is equals to X of minus t is satisfied then the signal is said to be even signal very simple how to write definition in terms of words as I said if the signal is symmetric about vertical axis it is known as even signal mathematical formula is X of T is equals to X of minus t now second case this diagram this is the case for continuous signal if you if you want to
write the equation mathematical equation for discrete signal make the things simple replace T by n this is the diagram for discrete event signal same from this diagram I have drawn this diagram same diagram in the form of pulses so if I want to write a mathematical equation for even which is discrete signal so for even a discrete signal it is X of n is equals to X of minus n what I did simply I changed variable T by n that's it now second case this is the diagram for order signal see again I have a
Dom one diagram and I will divide it into two parts say part A and Part B theoretically we can say that part A and Part B are having same area but they are opposite to each other that means party and Part B are anti-symmetric about vertical axis in this case both parts Part A and Part B are symmetric amount of vertical axis whereas party and Part B are anti-symmetric about vertical axis such signal is known as anti-symmetric or or a signal so it is anti-symmetric or odd signal now about the mathematical equation look at part
a part for part a time period is positive because this is zero time period of part A is at rhs said so time period is positive amplitude response also positive so for part a mathematical equation is plus X of plus T that means simply it is X of t for Part B time period is negative because part B is at negative time axis this is the negative time axis it is at LHS as well as amplitude is negative it is below this horizontal line so for Part B I can write a mathematical equation as since
amplitude is negative I will write minus X time period is also negative I will write minus t now the things are pretty simple if the mathematical condition I will write it over here if the mathematical condition X of T is equals to minus X of minus t then the signal is said to be or or anti-symmetric signal this is the diagram for discrete signal which I have done it from continuous time signal same logic if I want to write mathematical expression for discrete order signal then it is X of n is equals to minus X
of minus here so this is the mathematical equation for discrete or signal the second last type of signal is energy or power signal the definition of energy signal is if average normalized energy of a signal is non-zero and finite then it is energy signal Now what's the meaning of this average normalized average means we have to take average of the values per certain time period normalized means taking magnitude of the signal take more of signal which is normalized so if you calculate energy and average energy and if you take magnitude of that if such value
is not non-zero it should not be zero and if it is finite it should not be Infinity then it is known as energy signal everyone is aware energy is denoted by E and its unit is joules now you just have to remember only one definition if I want to write definition of a power signal just replace the word what I am doing see if average normalized power of a signal is non-jure and finite then it is a power signal very simple so just replace the word energy by power you will get the definition of power
signal and we know that power is denoted by P and its unit is a vat the last step of signal is deterministic or random signal as the name indicates deterministic means there should be some mathematical equation or lookup table what's the lookup table lookup table is the truth table so if the signal can be expressed by using any mathematical formula or truth table then it is known as a deterministic signal for example sine wave cosine wave triangular square root of all the signals whatever we are using in Practical cases are deterministic signal because mathematical formula
of such signals is available then if this is not the case means if you cannot represent it mathematically or by using any truth table it is known as a random signal just now I mentioned almost all signals whatever we are using is determine our deterministic signals then what's the example of random signal which cannot be represented by mathematical formula or lookup table a good example of random signal is a noise which cannot be predicted so nice is an example of a random signal so dear students this is all about the types of signals uh as
I mentioned these all these types of signals are very very important for the entire subject so thank you thanks for watching this video
