Consider the system describe by the difference equation y(n) = y(n 1) + x(n) + (n 1). (a) Determine its impulse

Consider the system describe by the difference equation y(n) = ½ y(n – 1) + x(n) + ½ (n – 1).

(a) Determine its impulse response.

(b) Determine its frequency response:

(1) From the impulse response

(2) From the difference equation

(c) Determine its response to the input x(n) = cos (π/2n + π/4) -∞ < n < ∞

(1) xt")=cos 10" + 3snGn +TO)