Question: A window w[n] is used to consider the part of a signal we are interested in. (a) Let w[n] = u[n] u[n 20]

A window w[n] is used to consider the part of a signal we are interested in.

(a) Let w[n] = u[n] − u[n − 20] be a rectangular window of length 20. Let x[n] = sin(0.1πn) and we are interested in a period of the infinite length signal x[n], or y[n] = x[n] w[n]. Compute the DTFT of y[n] and compare it with the DTFT of x[n]. Write a MATLAB script to compute Y(e^jω).

(b) Let w₁[n] = (1 + cos(2πn/11)) (u[n + 5] − u[n − 5]) be a raised cosine window which is symmetric with respect to n = 0 (non-causal). Adapt the script in the previous part to find the DTFT of z[n] = x[n] w₁[n] where x[n] is the sinusoid given above.

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a The DTFT of is The period of xn is 20 since the frequency is 220 The signal yn ... View full answer

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