A linear time invariant filter is described by the difference equation
*y*[*n*]=0.8*y*[*n*-1]-0.8*x*[*n*]+*x*[*n*-1].

1) Find H(z) and identify the poles and zeros.

2) Find an expression for the frequency response, assuming
*f*_{s}=44,100 *Hz*.

3) Show that the magnitude of the frequency response is 1 for all values of f.

*Solution.*

1)
The z-transform of *y*[*n*] is

Thus

2)

3)

Frequency response of the filter is shown in Fig.5.