Linear convolution
We compute the linear convolution of two causal signals with finite support.
Convolution is defined by
By dragging the coefficients of and , check that
- the response of a filter with impulse response to an impulse is ,
- the response of a filter with impulse response an impulse at index is the input shifted by samples,
- the convolution of two signals can be obtained by decomposing a signal as a sum of impulses, and adding the responses to these impulses.