Question: Recall that for integers M, H(ew) = ei M is the frequency re- sponse of a simple LTI system that implements a delay by

Recall that for integers M, H(ew) = ei M is the frequency

Recall that for integers M, H(ew) = ei M is the frequency re- sponse of a simple LTI system that implements a delay by M samples. Now consider an LTI system with frequency response H(ej) = ejwv5 for - w < . You might think of this as a system that implements a non-integer delay, but as mentioned in lecture, sequences x[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 x[n] = acos(won) + sin(won) for arbitrary real scalars a, , and wo. Based on the relationship between y[n] and x[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 quali- tatively based on your own opinions)

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