(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...
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# Non-Integer Delay

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 &lt; 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)

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