1. Consider an impulse response h[n] such that h[n] = 0 for n < 0 and...

   

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1. Consider an impulse response h[n] such that h[n] = 0 for n < 0 and n > M, and h[n] = -h[M-n] for 0 ≤ n ≤ M where M is an odd integer. a) Express the Fourier transform of h[n] in the form H(jw) = f(w) A (w), where f(w) and A(w) are real-valued functions of w. Determine f(w) and A(w). b) Provide an example of such an impulse response h[n] for M = 7 and find the corresponding f(w) and A(w). 1. Consider an impulse response h[n] such that h[n] = 0 for n < 0 and n > M, and h[n] = -h[M-n] for 0 ≤ n ≤ M where M is an odd integer. a) Express the Fourier transform of h[n] in the form H(jw) = f(w) A (w), where f(w) and A(w) are real-valued functions of w. Determine f(w) and A(w). b) Provide an example of such an impulse response h[n] for M = 7 and find the corresponding f(w) and A(w).

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Since hin 0 for n 0 and n M then hn 0 hM n hn for all n 0 and n M Now consider 0 n M Since M is ... View the full answer