A digital filter has has the following transfer function:
H(z)=(1-z^-1)/(1+.9z^-1)
(a)compute the magnitude response H(w), and phase response of the filter.
(b) determine the input-output relation(difference equation) of the filter in the time domain.
(c) compute the output of the system if the input is x(n)=2cos(πn/6 +45o) -∞