 Hello, everyone. I am K. R. Biradhar, assistant professor, department of electronics and telecommunication engineering, waltz engineering, stop technologies, salapo. Welcome to video lecture on classification of signals. Let us start with the learning outcomes first. At the end of this session, students will be able to identify deterministic or random and periodic or non-periodic signals. Find fundamental period of the signal. There are types of signals. The various types of signals are deterministic and random signal, periodic and non-periodic signal, energy and power signal, causal and non-causal signal, even and odd signal. In this video, I am going to discuss the first one and second one deterministic and random, periodic and non-periodic signal. First one is deterministic signal. A signal exhibiting no uncertainty of its magnitude and phase at any given instant of time is called deterministic signal. Example for this is sine wave. You can see this sine wave. We know that is nothing but we can predict any time we can what the signal appears. For example, there is a positive half cycle here. So, the positive half cycle repeats or comes again after certain interval of time. This you can predict it. This type of signal is called a deterministic signal. Next random signal. A signal characterized by uncertainty about its occurrence is called a random signal. A random signal do not have a that is standard mathematical equations. What I mean to say is I am speaking now. My vice is a random signal because I can pass, I can stop, I can raise my volume, I can reduce my volume. This you cannot predict. Nobody can predict what I am doing. That unpredictable is a signal is called a random signal. Even noise is also a random signal. We do not predict when it the what amplitude is going to come, what is what is its corresponding time etcetera. Before discussion of a periodic signal, we will come to know what is that term periodic means. Think and write your answer. Periodic means anything which repeats at regular interval of time. The term periodic means anything which repeats at regular interval of time. Periodic signal. A signal which has a definite pattern and repeat itself at regular intervals of time is called periodic signal. For example, it satisfies x of t is equal to x of t plus capital T for all t where small t denotes time and capital T denotes time period or fundamental period. So, you can see this example for a periodic signal. The first cycle will have a time period t. Second cycle also have a time period t. So, it is going to repeat. It has a particular that is definite shape and pattern. It repeats after particular interval of time. This type of signal is called the periodic signal. So, this x of t may also holds good for x of t plus capital T or x of t plus 2 capital T or x of t plus capital 3 t etcetera. The what is a fundamental period then? The smallest value of t which satisfies the condition x of t plus capital x of t is equal to x of t plus capital T is called fundamental period. That is simply time period. The reciprocal of fundamental period is its fundamental frequency. We know that is t is equal to 1 by f or f is equal to 1 by t. The angular frequency omega is equal to 2 pi f. If I substitute f is equal to 1 by t, it becomes 2 pi by t. If I take that is a t other side, this becomes t is equal to 2 pi by omega that is called the fundamental period. Non-periodic signal, a signal which do not repeat itself after a specific interval of time is called non-periodic or a periodic signal. So, if non-periodic signals should not satisfy the condition x of t is equal to x of t plus t. That means, x of t is not equal to x of t that type of signal is called the non-periodic signal. Example for this is you can see there is do not have a definite pattern and which will not repeat at regular interval of time. This is called the non-periodic signal in continuous time system. Important note the sum of two continuous time periodic signals x 1 of t and x 2 of t. There are two continuous time signals with their periods t 1 and t 2 t 2. If they sum it up, they may be are periodic or may not be periodic. If they are even though if they are they are those two signals x 1 of t and x 2 of t are periodic that sum may not be periodic or may be periodic. Second important note is the sum of two periodic signals is periodic only if the ratio of their respective periods that is t 1 by t 2 is a rational number or ratio of two integers. If you have a first signal period t 1 and second signal time period t 2 their respective ratio that is t 1 by t 2 is must be a rational number or ratio of integers then that type of signal is called the periodic signal. If the ratio t 1 by t 2 is an irrational number t 1 is a fundamental period first signal t 2 is a fundamental period second signal. If I divided those two if it is not a ratio of integers then it is an irrational number then that type of signal says a periodic or non-periodic. So, it do not have a common period and it is a non-periodic. In continuous time signal having exponential function is always periodic for example, e raise to j omega theta is always periodic in continuous time domain. Similarly, a discrete time signal x of n is periodic if it satisfies the condition x of n is equal to x of n plus capital N for all n. Here instead of t you need to take that is a discrete time signal n. So, where n is a positive integer integer which do not satisfy the above condition x of n is equal to x of n plus 1 n is non-periodic. The smallest value of n which satisfies the condition is called fundamental period and it is given by n is equal to 2 pi m divided by omega where m is an integer omega is a angular frequency. You can see this diagram this is a example for discrete time periodic signals having capital N capital N it itself repeats or this signal repeats at regular interval of time that is why it satisfies x of n is equal to x of capital N plus capital N that is why it is a periodic signal. Identify the periodicity of the signal consider this example x of t is equal to sin 2 t plus cos 3 t. Compare this one with sin omega t and this with cos omega t. Here first one you take omega 1 and second one you take omega 2 omega n is equal to 2 and omega 2 is equal to 3 we know the formula t 1 is 2 pi by omega. If I substitute that is nothing, but omega 1 is equal to it becomes t 1 is equal to pi here t 2 is equal to 2 pi by 3 then the ratio t 1 by t 2 is 3 by 2 this is a rational number therefore, it is a periodic signal what is this fundamental period we know cross multiply these two it becomes 2 t 1 and 3 2 t 2 therefore, fundamental period t is equal to 2 t 1 is equal to 3 2 t 2 this is equal to 2 into t 1 is pi then 2 pi therefore, fundamental period our time period is equal to 2 pi. Second one you consider the discrete time example x of n is equal to cos n by 6 into cos of n pi by 6 here again you compare with cos omega n omega 1 is equal to 1 by 6 and omega 2 is equal to pi by 6 therefore, we know the formula 2 pi m divided by omega substitute becomes 12 pi and becomes equal to 12 by considering minimum value of m which is equal to 1 m must be an integer. Then the ratio is equal to pi so, the ratio is not a non integers or it is an irrational number therefore, it is a non periodic signal. Next example is x of n is equal to sin of 0.02 pi n omega is equal to 0.02 pi so, n is equal to pi by m divided by omega you know if I substitute you are going to get that is n is equal to 100 by considering m is equal to 1 therefore, it is a rational number therefore, it is a periodic with fundamental period n equal to 100. Next example x of t is equal to sin of t plus 1 plus cos of root 3 t here omega 1 is equal to 1 and omega 2 is equal to root 3 t 1 is equal to 2 pi and t 2 is equal to 2 pi by root 3. Then the ratio t 1 by t 2 is equal to root 3 therefore, it is an irrational number this is a non periodic signal. If it is non periodic signal we need not necessary to calculate in its fundamental period. These are the references I have considered to prepare above pi by t. Thank you.