5. (Non-Integer Delay) Recall that for integers M, H (6”) = e'jwM is the frequency response

of a simple LTI system that implements a delay by M samples. Now consider an LTI system

with frequency response H (ejw) = e‘j‘m/E for —7r S w < 7r. You might think of this as a

system that implements a non-integer delay, but as mentioned in lecture, sequences a:[n] are

not deﬁned for non-integer values of n. (a) Consider the output y[n] that you obtain from this system when the input is m[n] 2

oz cos (won) + 6 sin(w0n) for arbitrary real scalars oz, 6, and can. Based on the relationship

between y[n] and :L'[n], are you satisﬁed with calling this a “non-integer delay” system? (b) Compute the impulse response h[n] of this system. (c) Based only on the impulse response, are you satisﬁed with calling this a “non-integer

delay” system? (This is a subjective question — you should answer qualitatively based

on your own opinions)