A linear time-invariant system is described by the difference equation(a) Find the frequen...

A linear time-invariant system is described by the difference equation

(a) Find the frequency response  then express it as a mathematical formula, in polar form (magnitude and phase).

(b)  is a periodic function of  determine the period.

(c) Plot the magnitude and phase of  as a function of  for –π< > 3π. Do this by hand, and then check with the MATLAB function freqz.

(d) Find all frequencies , for which the output response to the input  is zero.

(e) When the input to the system is x[n] = sin(7πn/13), determine the output signal and express it in the form