why always impulse response?

impulse response

what is meant by impulse response? why we use it to study to character of the signal that is study the linearity,stability etc? why it is called ideal system to study?

plz help i hav read signa sys,control etc but i hav yet not understand this problem

To characterise the frequency response of any system one needs to apply signal that has same strength at all frequencies. Only then the proper frequency response of the system can be fond out.

Animpulse in tme domain has the characteristics that at all frequrncies from 0 to ∞ the signal amplitude is same.

So an impulse response is essential.

In addition to the explanation of SUBHARPE there is a nice and simple relationship with the transfer function T(s) of a system:

The impulse response h(t) is the inverse LAPLACE transform of T(s) - or vice versa:
T(s)=L(h(t)) . This property is important for designing some kinds of digital filters.

these two reasons are synonymous.

subharpe said:

these two reasons are synonymous.

Click to expand...

Yes, but are you sure that everybody knows ?

If a pattern is seen in many particular problems which can be solved by similar solutions, it makes sense to consolidate the tools under a common heading.

Same is true for LTI theory. The theory is a collection of tools that solve many problems of concern. Of course, nothing is exactly as our nice little mathematical model and approximation holds under some conditions (which we are OK with usually).

So much for the state of affairs. Now for the impulse response:

We are usually concerned with the response of a system to input signal. Now, since the system is linear you can analyze the response if you do it by breaking the signal in pieces (time shifted impulses). Now, as the system is time invariant you just need to know the response of the system to an impulse located at 0.
So, the response of the LTI system to δ(t) is sufficient to know all that the system can do to any arbitrary signal.

If you break up signals in complex exponentials and that is the frequency analysis.

I'd recommend Oppenheim Schafer's signals systems book if you have more such doubts. Best would be to use it in conjunction with Lathi's signal processing book.

In the above answers, system linearity has been assumed by all contributors. sayurabh's question however also addresses nonlinear effects. Of course, the said simple duality of frequency and time domain can be applied to linear systems only.

When analyzing real systems, that usually have finite linearity, impulse response is most interesting when time domain behaviour is the primary quality criterion, e.g. for pulse amplifiers. For other applications, large signal sine wave reproduction, measured as THD or IM may be more important.

It's effectively impossible to reveal small linearity errors from an impulse response measurement, even with nearly perfect pulse generators. But a two-tone measurement can do rather easily.

In addition, even for systems, that aren't primarly used with pulse signals in normal operation, impulse response can be still a valuable test.

The most important characteristic of the impulse response is that when we know it we can simply find the response of the system to every input. This can be done by convolving the input with the impulse response.