The deterministic crosscorrelation function between two real sequences is defined as...

The deterministic crosscorrelation function between two real sequences is defined as

(a) Show that the DTFT of c_xy[n] is C_xy(e^jω) = X(e^jω)Y^∗(e^jω).

(b) Suppose that x[n] = 0 for n < 0 and n > 99 and y[n] = 0 for n < 0 and n > 49. The corresponding crosscorrelation function c_xy[n] will be nonzero only in a finite-length interval N₁ ≤ n ≤ N₂.What are N₁ and N₂?

(c) Suppose that we wish to compute values of c_xy[n] in the interval 0 ≤ n ≤ 20 using the following procedure:

(i) Compute X[k], the N-point DFT of x[n]

(ii) Compute Y [k], the N-point DFT of y[n]

(iii) Compute C[k] = X[k]Y^∗[k] for 0 ≤ k ≤ N − 1

(iv) Compute c[n], the inverse DFT of C[k] What is the minimum value of N such that c[n] = c_xy[n], 0 ≤ n ≤ 20? Explain your

reasoning.