We studied about infinite impluse response and finite impulse response of a systems. Also we say that it is non realistic function... then why we study this
In all systems, impulse response is a means to study the system behavior and performance. If the system is stable, then it allows us to quantify the quality of stability, for example. For linear time invariant (LTI) systems, impulse response completely defines the system behavior and is equivalent to transfer function of the system. So it is often used for system identification purposes in engineering applications. This is why we study impulse response.
Transient response is good sir... why we needs to model it using a unrealistic function...... i too agree that for linear system impluse response is the system function
It can be viewed as a perturbation, and it will help you to see how your system responds to sudden change. If you know how your system reacts to it, then you can calculate the reaction to other inputs as well, given your system is linear time-invariant.
However, impulse response is not the only way to characterize a system, step response, ramp response, and so on are also used, and in some cases they are used together.
An impulse is represented by a Dirac's delta function. The delta function contains all Fourier components. Therefore, you can reproduse any responce of the system as you analyse the responce to the impulse.
If you still don't understand, study about Fourier transformation. This is crucially important to understand control theory. God luck.