(a) Consider the system of Figure P10.24-1 with input sampling period
T = 10−4, and
What is the smallest nonzero value of N such that Xw[k] is nonzero at exactly one value of k?
(b) Suppose now that N = 32, the input signal is and the sampling period T is chosen such that no aliasing occurs during the sampling process. Figures P10.24-2 and P10.24-3 show the magnitude of the sequence Xw[k] for k = 0, . . . , 31 for the following two different choices of w[n]:
Indicate which figure corresponds to which choice of w[n]. State your reasoning clearly.
(c) For the input signal and system parameters of part (b), we would like to estimate the value of _0 from Figure P10.24-3 when the sampling period is T = 10−4. Assuming that the sequence and that the sampling period is sufficient to ensure that no aliasing occurs during sampling, estimate the value of . Is your estimate exact? If it is not, what is the
maximum possible error of your frequency estimate?
(d) Suppose you were provided with the exact values of the 32-point DFT Xw[k] for the window choices w1[n] and w2[n]. Briefly describe a procedure to obtain a precise estimate of .
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