Show that the periodogram values at frequencies f k = k/L, k = 0, 1. . .

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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.

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Digital Signal Processing

ISBN: ?978-0133737622

3rd Edition

Authors: Jonh G. Proakis, Dimitris G.Manolakis

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Question Posted: May 26, 2011 02:59 AM

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Show that the periodogram values at frequencies f k = k/L, k = 0, 1. . .

Question:

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

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