Show that the periodogram values at frequencies f_k = k/L, k = 0, 1. . . L ? 1, given by (12.1.41) can be computed by passing the sequence through a bank of N IIR filters, where each filter has an impulse response?

Hk(n) = e ^?j2?k/Nu(n)

and then compute the magnitude-squared value of the filter output at n = N. Note that each filter has a pole on the unit circle at frequency f_k.

N-1 7/ws21-(4)x k = 0. 1... L-1 P (t) - E (n)e-120m, (12.1.41)