A discrete-time linear and time-invariant (LTI) system is given by the following input-output relationship: y[n] = 2x[n] − x[n − 1], where x[n] is the input and y[n] is the output.
(a) What is the frequency response?
(b) What is the response of the system to input signal 1 + e^(j*(pi/2)*n)
For the problem above, I figured out that the frequency response is H(jw)=2-e^(-jw). So for the new response in part b, I know that x[n]= e^(j*0*n) + e^(j*(pi/2)*n). How should I proceed from here?