Convolution

Abstract

If we know a system’s impulse response, we can calculate the output of that system for any input. The impulse response is defined here as the output response to the unit impulse input to a linear system. The calculation of the output based on the input and the impulse response is called convolution defined in the time domain. The same calculation can be carried out in the frequency domain using the Fourier and inverse Fourier transforms. The reason we use this roundabout method is because the output is obtained in much shorter time than by directly calculating the convolution integral in the time domain.