 Hello everyone, welcome to this session. I am Deepali Vardhakar working as an assistant professor at WIT, Solapur. In this lecture we are going to discuss the classification of the system and this is the part one. At the end of this session student will be able to classify system. These are the content, signal and system definition. We will discuss examples of system, then the classification of system in that we are going to discuss continuous time and discrete time system, static and dynamic system. Before moving ahead, let us recall the signal. The signal is the function of one or more variables that conveys the information about some physical phenomena. Examples of signals are a voltage, current, any x t signal, heartbeats, blood pressure, temperature. So, there are number of examples of signals. These signals are one dimensional as well as two dimensional system. It is the device or combination of devices which can operate on signals and produces corresponding response. This input to the system it may be one or more than one. So, this input is nothing but called as an excitation and output from the system it is generally called as a response. So, in this example x t or x of t it is the input to this system, y of t it is the output from this system. Practically, this system can be represented as y of t is equal to transpose of x of t. So one of the example of the system it is nothing but CRO. Here the input to this CRO is provided through this function generator which is f of t. Now, this CRO which is act here as a system and transforms this input from function generator into output in the form of image and this image is displayed on the CRO. Here the output it is nothing but S of x, y and it is independent variable for this output it is space and for the input independent variable is nothing but time. So, this is the one of the example of a system which transforms the input from the function generator into image on the CRO. Let us see the classification of the system. The first system is classified into continuous time and discrete time system, then static and dynamic, then causal and non-causal systems, linear and non-linear systems, time variant and time invariant systems, stable and unstable systems, invertible and non-invertible systems. So, this is nothing but classification of the system. System is a continuous time when its input and output signals are continuous time. So, for this type of system the input signal suppose x of t it is continuous and y of t is also continuous. Such systems are called as a continuous time system. Now let us see one of the example of continuous time system. So, here the process of measuring the temperature of the room, here the temperature monitoring system measures the temperature of this room continuously. So, we can say that this system is a continuous time system. The another example of continuous time system it is nothing but this RC series circuit. Here v s of t it is nothing but input voltage, v c of t output across the capacitor, output voltage across the capacitor. Now by using the Ohm's law we can find the relation between the current and voltage across the capacitor and the relationship of current and voltage for the capacitor it is nothing but i of t is equal to c d dt v c of t. So, by using this two relation we can find the relation between the input voltage and output voltage. So, this circuit or this system is represented by using this equation. So, this is the relation between the output voltage and input voltage. So, input voltage is a input v s of t and output is voltage across this capacitor v c of t. So, this is the one of the example of continuous time system. So, the voltage across this capacitor varies according to the input voltage. Now the next is a discrete time system. The system is a discrete time when its input and output signals are discrete. So, here for this system x of n it is in the form of discrete. So, output of this system is also in the form of discrete value. Let us see one example. In this example the temperature monitoring system which measures the temperature of the room only at particular interval of the temperature is measured suppose at 1 o'clock, 2 o'clock, 3 o'clock, 4 o'clock like that. So, for n value of 1, 2, 3 here the temperature values are given. So, if the temperature is measured at a particular interval of time then that system temperature monitoring system is called as a discrete time system. Then the static and dynamic system, the static system it is the memory less if its output at any instant depend on the input at that instant, but not on past and future values of input. So, let us see the example of static system. Here y of t is equal to 2 into x of t. In this equation put t is equal to 0 then the system output is y of 0 is equal to t into x of 0. Put t is equal to 1 the system output is y of 1 is equal to 2 into x of 1 put t is equal to minus 1, the system output is y of minus 1 is equal to t 2 into x of minus 1. So, if you observe the output only depend upon the value of present input means x of t ok. So, hence here the output is only depend upon the present input, hence this system is a memory less or static. Let us see the another example for static system y of t is equal to t into x of t. So, put t is equal to 0 here, the system output y of 0 is equal to 0 into x of 0 which is equal to 0. If you put t is equal to 1, the system output is y of 1 is equal to 1 into x of 1 which is equal to x of 1. Put t is equal to minus 1, the system output is y of minus 1 is equal to minus 1 into x of minus 1 which is equal to minus x of minus 1 ok. So, here again the output only depend upon the present input ok. So, hence the system is a memory less or static ok. This is the third example y of n is equal to 9 into x of n. Here the output at n in instant that means y of n depend on the input at nth instant ok. So, we can say that this system is also static system. This is the example of discrete static system. Then the dynamic system it is the system in which the output at any instant of time depends on input samples at the same time as well as the other time ok. So, here the other time means this output is depend on present as well as past and future ok. So, if such systems are there the output may be depend on present, may be depend on past or may be depend on future. So, in that case that systems are called as a dynamic systems. So, let us see the example here y of t is equal to 2 x of t plus 3 x of t minus 3 put t is equal to 0. The system output is y of 0 is equal to 2 into x of 0 plus x of 3 into x of t here 0. So, 0 minus 3 minus 3 ok. Put t is equal to 1 here the system output is y of 1 is equal to 2 into x of 1 plus 3 into x of 1 minus 3 that is the minus 2. Then put t is equal to minus 1 the system output is y of minus 1 is equal to 2 into x of minus 1 plus 3 into x of minus 1 minus 3 means minus 4 ok. So, if you observe all these here the output y of t is depend on present and past input. So, these systems is nothing but dynamic system. The another example for a discrete dynamic system here y of n is equal to x of n plus 6 into x of n minus 2 ok. So, here the output at any nth instant depend on the input at nth instant. If we put the value of n is equal to 0 and is equal to 1 and so on here the output at any nth instant is depends on input at nth instant as well as input at x minus 2 second instant ok. So, it is depend upon the present as well as previous sample output. So, this type of system is called as dynamic systems. Now, we will think on this one question why the dynamic systems has a memory ok. So, here if you observe the input output relation of dynamic system here the output depends on past and future input sample. So, we need a memory to store such sample ok. So, these type of systems are required or has a memory ok. So, the dynamic systems has a memory. So, these are the references. Thank you.