Show that the IDFT of X[k] defined in Exercise 13.9 gives x[n] in (13.45). Furthermore show that…

Show that the IDFT of X[k] defined in Exercise 13.9 gives x[n] in (13.45). Furthermore show that the signal x[n] obtained via the IDFT is periodic with period N.

Exercise 13.9

Use the results of Section 13-5.5 to determine an equation for the 40-pt. DFT of flu] in (13.45). Verify that some of the nonzero DFT values are

 

What are the other nonzero values of X[k]? For which indices k are the DFT coefficients X[k] equal to zero?