why is impluse function so useful in linear systems?what is the reason of it's power?

Answer 1

The respnse of a system to a unit impulse is the defining characteristic of the system. Electronic systems are often designed in the frequency domain usling the Laplace transform of the impulse response to describe the system. This is called the transfer function H(s) where s is the complex frequency (frequency and phase). It is easier to compute the response of a network in terms of the transfer functions of its components because the result contains products and ratios of the transfer functions rather than complex integrals. Ultimately, the way the system behaves is described by it's impulser response. See http://en.wikipedia.org/wiki/Impulse_response

Answer 2

The impulse function is useful because it allows you to get the impulse response. The impulse response is how a system reacts if an impulse is sent through it. The impulse response which is H(f)or H(jw). Once you have the impulse response you can determine any output by Y(f)=H(f)X(f). Here is one of the best sites on the web about signals and systems.It is a web site for the book "Signals, Systems, and Transforms" by Phillips, Parr, and Riskin. Good book but don't try to read it unless you have taken some electrical engineering classes or you will be LOST.
http://www.ee.washington.edu/class/235dl/