The convolution of the input signal with the impulse response of the system yields the output of the system, regardless of the input waveform. Easiest carried out in the s domain, since multiplication (any easy task) in the s domain is equivalent to convolution (a difficult task) in the time domain.
You can think about the convolution as this :
Imagine your signal as a well ironed piece of CLOTH and your system as a piece of PIPE with several degrees of bends .Passing the piece of CLOTH trough all pipe and this one comes out all WRINKLED ..but is difficult to make a sens out it what bend of the pipe did what WRINKLE .. But in the frequency domain is very simple because it amounts to a linear operation a simple MULTIPLICATION
Convolution is one of the primary concepts of linear system theory. It answers the problem of finding the system zero-state response due to any input - the most important problem for linear systems.
The main convolution theorem states that the response of a system at rest (zero initial condition ) due to any input is the Convolution of that input and the system impulse response.
convolution is a process by which we get the response (ie.) of a LTI system
with any given input.convolution is integral process which is difficult in some cases.we transform into s or freuency domain.i transform domain convolution transforms to multiplication.
the easiest way of explaining the convolution in discrete signals is.. just the process of polynomial multiplication.. suppose u convolute [3 1 2] and [ -4 9 6] then they are just coefficients of polynomial obtained by mul 3*x^2 + x + 2 and -4*x^2 + 9*x + 6 or so... this could give u some idea incase u dnt know.
The convolution of the input signal and the impulse response of a LTI sistem respectibly , is the output signal of the LTI system, the convolution in the frecuency is the multiplication of the signal ant he impulse response.
LTI system meas a system which its response to a wave is not change when the signal shifted. its response is only shifted due to amount of shifting in original signal. so if you think of your input as a sum of some shifted delta dirac function ,which its ampilute is determined by your function,(in continous form the sum is integral) the out put of your system will be sum of system shifted response of your system to delta dirac function(also in continous form the sum is integral). this leads to definition of convolution.