On the poly-phase filter banks, it's straightforward to use the Goertzel agorithm instead of DFT can reduce the costs if only one user is to be extracted. In the Tim Hentschel and Tuttlebee's book and some related articles, there're some discussions on this topic. The following link is available, related discussions on p.p. 31. http://citeseer.ist.psu.edu/hentschel02channelization.html While I check this algorithm, I found a question. The goertzel algorithm is a single-pole IIR filter, which means that this filter has a very narrow frequncy response at the pole bin. This can be easily simulated and confirmed by MATLAB. So, when I use the goertzel algorithm to exract a band-limited channel, the result is that, there is a 'pole frequency response' at the corresponding pole of goertzel filter. And the extracted user band is heavily distorted. This can be seen on the picture follows.The pciture is to extract a chirp signal from Band 0 of a 8-equal distributed band within a wideband(original intention is to simulate a uniform DFT filter banks). The polyphase branches and the decimation number is M=8. In the goertzel on the figure, k =0.1, N =8. on exp(-j*2*pi*k/N). The pole distortion is at point ''A'' on the figure. | | | | | --------. | ------| | '\ .' | | \. | | | \ |' | | '. | | | \ | | | \ | | | '. | | | \ .' | | ---------------' | --------------------------------------------|- o 1 Original Chirp Signal Spectrum | || | || | || | .|| | --|||---. | ------| | A '\ .' | | \. | | | \ |' | | '. | | | \ | | | \ | | | '. | | | \ .' | | ---------------' | --------------------------------------------|- o 1 Band signal extracted by using Goertzel algorithm (created by AACircuit v1.28.6 beta 04/19/05 www.tech-chat.de) So, I think, the goertzel algorithm can be used to extract a single-tone on channelization, not suitable for a band-limited user. But, On the channelization theory, the goertzel algorithm applied here is just an operation, it's to substitute the frequency modulations on H(K), so, it should has similar effects compare with DFT operations.While the result is not.This question confused me a long time, I wonder if you smart guys can give me some clues. Sun Lei.

# on extracting band-pass signal by using Goertzel algorithm instead of DFT filter banks

Started by ●June 28, 2007