x[n] is a finite-length sequence of length 1024, i.e., x[n] = 0 for n < 0, n...

x[n] is a finite-length sequence of length 1024, i.e.,

x[n] = 0 for n < 0, n>1023.

The autocorrelation of x[n] is defined as

and X_N[k] is defined as the N-point DFT of x[n], with N ≥ 1024.

We are interested in computing c_xx[m]. A proposed procedure begins by first computing the N-point inverse DFT of |X_N[k]|² to obtain an N-point sequence gN[n], i.e.,

(a) Determine the minimum value of N so that c_xx[m] can be obtained from g_N[n]. Also specify how you would obtain c_xx[m] from g_N[n].

(b) Determine the minimum value of N so that c_xx[m] for |m| ≤ 10 can be obtained from g_N[n]. Also specify how you would obtain these values from g_N[n].