 Hello everyone, I am K. R. Viradhar, Assistant Professor, Department of Electronics and Telecommunication Engineering, W. I. T. Salafow. Welcome to a video lecture on Types of Discrete Time Signals. Let us start with the learning outcomes first and then end of this session students will be able to know different ways of representing discrete time signals, classify various forms of discrete time signals. These are the some of the contents start with representation of discrete time signals, basic types of discrete time signals and references representation of discrete time signals. There are four different forms of representing discrete time signals, they are graphical representation, functional representation, tabular representation, sequence representation. Representation of above four methods are explained by taking one example each. Consider a signal x of n with values x of minus 2 is equal to minus 3, x of minus 1 is equal to 2, x of 0 equal to 0, x of 1 is equal to 3, x of 2 is equal to 1, so on. So, different values of n which varies from minus 2, minus 1, 0, 1, 2, 3 and corresponding value of x of n minus 3, 2, 0, 3, 1, 2 are represented using first method graphical method along the x axis you need to consider the values of n which varies from minus 2 to plus 3 along the y axis you need to take the values of n. Every value of n that is for example minus 2 the corresponding value of x of n. Similarly, n is equal to minus 1 corresponding value of x of n will be 2. Similarly, at 0 it is a separation or origin of this sequence at n equal to 0 it is x of n is 0, so on. So, second method of representation is functional representation in functional representation x of n minus 3, 2, 0, 3, 1, 2 and corresponding value of n for n is equal to minus 2 its value is minus 3, n equal to minus 1 its value is 2. So, the corresponding different values of n the corresponding value of x of n will be given. Next is tabular representation. In tabular representation we need to consider the n in first row and x of n in second row. So, different values of n the corresponding value of x of n will be representation. Next one is sequence representation. If I need duration sequence can be represented as x of n is equal to minus 3, 2, 0, 3, 1, 2. This arrow indicates that is origin of the signal. So, towards right or called the that is n equal to 1, 2, but towards left is called the n equal to minus 1, minus 2, minus 3, etc. This is a sequence representation. Recall what are the different methods of continuous time signals we have seen. Pause in this video for a moment and think of what are the different types of continuous time signals. The different types of continuous time signals are start with the step signal and ramp signal, parabolic signal, etc. The same signals we are going to study using discrete time signals. The basic types of discrete time signals. First one is unit step signal. So, unit steps signal will be represented by u of n and it is defined as u of n is equal to 1 for n is greater than or equal to 0, 0 for n less than 0. So, this is a sequence. You can see that is along the exact state n corresponding u of n. We have different values of n corresponding value of u of n. So, n equal to 0 that is 1, n equal to 1 also 1 and this varies from n varies from 0 to plus infinity its values are 1. But whereas in the negative side you do not find any signals, then because n is less than 0 its value is 0. Next one is unit ramp signal. Unit ramp sequence will be represent by r of n and it is defined as r of n is equal to 1 for n is greater than or equal to 0, 0 for n is less than 0. You can see this graph along the x axis we need to consider n along the y axis is r of n. For a different values of n corresponding r of n will be written. So, if for example, if I substitute n equal to 0 its value is 0 only at origin if I substitute n equal to 1. So, r of 1 is equal to 1 that is first sequence is 1. Similarly, if I substitute n equal to r of 2 is equal to 2 you can see the second sample. Similarly, n equal to 3 then r of 3 is equal to 3 keep on that varies from 0 to plus infinity. Whereas in the negative side n is less than 0 its value is 0. We need not consider that is not negative side only positive side which varies from 0 to plus infinity samples will be present. Next one is unit impulse sequence. The impulse sequence will be represent by delta n. It is very simple delta n can be defined as its existence only exists only at n equal to 0 otherwise its value is 0. You can see this graph along the x axis you can see that is minus infinity n varies from minus infinity to plus infinity its value is 0. So, all other places except at n equal to 0. So, this type of signal is delta n you can this can be used for that is nothing but many applications in digital signal processing. Next unit parabolic function. Unit parabolic function is represented by d of p of n discrete time parabolic function is defined as p of n is equal to n square by 2 for n is greater than r equal to 0 0 for n is less than 0. In terms of step function it can be written as p of n is equal to n square by 2 into u of n. This is a relation between unit parabolic function and the step function p of n is equal to n square by 2 into u of n. Along the x axis you can see its value of n along the y axis is a p of n. The different values of n we have considered 0 to plus infinity this side is 0 to minus infinity we are not looking for any that is n which varies from minus 1 to minus infinity because its value is 0 whereas for plus side it is if I substitute n equal to 0 it is 0 by 0 it is sampled to 0. If I substitute n equal to 1 that is 1 by 2.5. If I substitute n equal to 2 that is 4 square 2 square means 4 4 divided by 2 is 2. So, this is a that is the signal for unit parabolic function. This is the relationship between parabolic and the unit step function. Next in a sinusoidal signal the discrete time sinusoidal sequence is given by x of n is equal to a sin omega n plus pi where a is the amplitude omega is the angular frequency and pi is the phase in angle in radians. You can see this graph along a discrete time signal that is a which represents a sin omega n bar. Note for a discrete time signal to be periodic the angular frequency omega must be a rational multiply of 2 phi. The time period of the discrete times sinusoidal signal is given by n is equal to 2 pi m divided by omega. You can calculate that is in our time period for a discrete time signal using this formula where n is an integer. So, next discrete exponential signal or discrete exponential signal is defined as x of n is equal to a raised to n for all the n. So, you can see this x of n is equal to a raised to n. Here first 2 graphs which way which varies from that is nothing but this a is greater than 1. You can see this there is a graph which growing exponentially. If way varies from 0 to 1 if it is graph as samples which decaying exponentially. Similarly, if a is less than minus 1 you can see that is alternatively samples are switching from plus to minus. So, this is a is between minus 1 to 0. This is a case that is same thing as it is decaying switching the samples alternatively. These are the same references I have considered. Thank you.