Computing the Fourier series coefficients for a Discrete Time signal x[n]
The System
$ y[n] = x[n] + x[n-1] + x[n-2] + x[n-3]\, $
Unit Impulse Response
$ x[n] = \delta[n]\, $
$ h[n] = \delta[n] + \delta[n-1] + \delta[n-2] + \delta[n-3]\, $
$ y[n] = x[n] + x[n-1] + x[n-2] + x[n-3]\, $
$ x[n] = \delta[n]\, $
$ h[n] = \delta[n] + \delta[n-1] + \delta[n-2] + \delta[n-3]\, $