 Hello everyone. Myself K.R. Biradhar, assistant professor, department of ENTC, WIT-Solapore. Today I am going to discuss the topic on continuous time and discrete time signals. Let us start with the learning outcomes first. At the end of this session, students will be able to define various types of signals, differentiate CT and DT signals that is continuous time and discrete time signals. These are the some of the contents. Introduction to signal and system that is definition of signal and system. Continuous time signal and discrete time signal. Types of continuous signals, lastly references. Signal and system. A signal is defined as a physical quantity that varies with time, space or any other independent variable. For example, what I am speaking now is, is a speech signal or voice signal is an continuous time signals. Variation of room temperature. For example, continuously temperature will vary independent of the time or irrespective of the time. That is also example for continuous time signals. Then what is the system? System is a meaningful interconnection of physical devices and components which act together. That means, so all the elements of a system are arranged in such a way that which acts together, which should perform a particular task that you can call it as a system. Next, move on to the next slide. That is continuous time signal and the discrete time signals. There are two types of signals that is continuous time and discrete time signal. Then first one is the signals that are continuous in time and continuous in amplitude are called continuous time signals. Example for this is a sine wave. Let us see this wave form. It is a sine wave. Along the x axis you can find the time. Along the y axis it is an amplitude. So, along the x axis time is an independent variable but even it is continuous in nature. Whereas amplitude also it is continuous in. That every instant of time there is an amplitude. That means it is continuous in nature. Whereas in other form of signal that is discrete time signal. So, signal amplitude is present only at discrete intervals of time. Let us see that also. So, a signals that are discrete in time and continuous in amplitude are called discrete time signals. Along the x axis it is an n. Along the y axis it is x n. Continuous time signals are represented by x of t versus t. Whereas discrete time signals are generally represented by x of n versus n. So, n is an index here. Along the x axis you can see index. For every discrete values of n you are getting corresponding value of x n that is an amplitude. In the previous case it is different. That is t is continuous. Every instant of time you are going to get the signal x of t. Next question arises whether discrete time and digital signals are same? Answer is no because let us see the digital signals in the next slide. In digital signals we can find there are discrete time and discrete amplitude. So, in discrete time signals what you have seen is it is discrete time continuous amplitude. Every instant of time interval of time there is an amplitude but amplitude is not constant. Whereas in digital signals you are going to find it is a constant amplitude samples that is 5 volt. But here it varies from 0 to 5 volt. That means every instant of interval you are going to get the amplitude at the high or low. That is high is always constant that value is 5 volt. But discrete time signal you are going to get the different values of amplitude. That is the only difference between digital signals and the discrete time signals. Next classification of continuous time signals. What are the basic classification? How we are going to classify the continuous time signals? First one is unit step function which is defined as u of t is equal to 1 for t is greater than or equal to 0. For 0 for t is less than 0. That means you can see this diagram unit step function along the x axis it is t along the y axis u of t. u of t value is 1 that is unit step it is. So, its value is present only for t is greater than or equal to 0. Even if t is equal to 0 u of 0 is equal to 1. If t is equal to 1 then u of 1 is equal to 1. If t is equal to 2 3 4 up to plus infinity its value is always constant is equal to 1. Whereas from 0 to minus infinity left hand side of this waveform you are not going to get the any value. That means if you substitute the value t is equal to minus 1 minus 2 minus 3 up to minus infinity. You are going to get the 0 steps signal present only at positive side of the waveform. Unit RAM signal which is defined as r of t is equal to t for t is greater than or equal to 0 0 for t is less than 0. That means here r of t or amplitude is present only between 0 to plus infinity. r of 0 if I substitute value will become 0. If I substitute t is equal to 1 r of 1 is equal to 1. If I substitute t equal to r of 2 is equal to 2. Then the values is present only and the right hand side of this waveform starts from 0 up to plus infinity. If I substitute a plus infinity r of infinity is equal to infinity. Along the negative side of this waveform you are not going to get the any values. Its value is defined as 0 irrespective of t minus 1 minus 2 minus 3 up to minus infinity. Next is unit parabolic signal which is defined as x of t is equal to t square divided by 2. For t is greater than or equal to 0 0 for t is less than 0. That means along the x axis if you consider t along the y axis it is x of t. Keep on substituting the value of t which varies from 0 to plus infinity. So for example if I substitute t is equal to 0 x of 0 is equal to its value 0. If I substitute t is equal to 1 x of 1 is equal to 1 square that is 1 divided by 2.5. If I substitute t is equal to that is 2 square is 4 divided by 2 its value is 2. Keep on increasing up to plus infinity. Whereas from the negative side again it is 0 irrespective of value of t. t may be minus 1 minus 2 minus 3 up to minus infinity. Its value is x of t will become equal to 0. Impulse function which is defined denoted by delta t and it is defined as delta of t is equal to 1 for t is equal to 0 0 otherwise. That means delta impulse function is present only at t is equal to 0. Any other places its value of t its value is 0. Next signum function signum function is defined as g n of t which is equal to 1 for t is greater than 0 0 for t is equal to 0 is equal to minus 1 for t is less than 0. Its value is 1 that means you can see the waveform. So from 0 to plus infinity its value is constant which is equal to 1 for t is greater than 0. Value 0 for t is equal to 0 along the negative side its value is always minus 1 that is t is less than 0. So, which up to 0 it is minus 1 at 0 it is 0 again from 0 to infinity t is plus 1. Next one is exponential function which is defined as x of t is equal to e raised to a t. So, a waveform depends on the value of a if a is equal to 0 a is greater than 1 and a is less than 1. So, if I say a is equal to 0 that becomes a DC signal if I say a is greater than 1 it is continuously or exponentially growing signal if I say a is less than 1 it is exponentially decaying signal. See the waveform t versus x of t if I substitute a value 0 then x of t is equal to e raised to 0 which is equal to 1 it becomes amplitude equal to 1 it is a constant signal or DC signal. In the figure b exponentially growing signal if I substitute the value of a which is greater than 1 then depends on the value of a depends on the value of a and t then you are going to get the continuously growing signal or exponentially growing signal. If I substitute t is equal to minus 1 it becomes very low low low if I substitute the value t is plus 0 to infinity then its value is growing or exponentially whereas, for a is less than 1 it is a decaying signal along the negative side of the waveform you can see the value of t is minus that is why if I multiply a minus with the value of a which is less than 1 then you are going to get the exponential rising towards as you go towards right side it is going to become 0 0 then if I substitute e a is equal to 0 then its value is 1 if I substitute t is equal to 2 3 4 up to etcetera plus infinity its value is decaying that means exponentially decaying signal these are the some of the references I referred thank you.