A linear time invariant filter is described by the difference equation y[n]=0.8y[n-1]-0.8x[n]+x[n-1].
1) Find H(z) and identify the poles and zeros.
2) Find an expression for the frequency response, assuming fs=44,100 Hz.
3) Show that the magnitude of the frequency response is 1 for all values of f.
The z-transform of y[n] is
Frequency response of the filter is shown in Fig.5.