i would a confirm of this: with polyphase structure is possible only design a filter bank with a INTEGER oversampling ratio? For non-integer i've seen the weighted overlap-add metod, is right?

thanks S.


If you have a 1D uniform $M$-channel multirate filter bank (FB), and $N$ is the decimation ($M \ge N$), rational oversampling ratios ($M/N$) are indeed possible (see Fig. 2), or from Figure 1 in Optimization of Synthesis Oversampled Complex Filter Banks, J. Gautier et al., IEEE Trans. Signal Processing, 2009 (doi), which provides optimized synthesis FB with any ratio (like $7/4$).

More precisely: for an analysis filter bank, you can choose any decimation you want. But you may loose information, and the invertibility of the analysis/synthesis system. In a lot of practical applications (for instance in speech processing), integer oversampling ratios are quite common, by choosing $N = M/k$, for instance $k=M/2$ or $k=M/4$. Such choices make the computations and some calculations much simpler: for instance, an inverse synthesis filter bank may take a closed form, related to the analysis window for DFT FBs.

However with redundancy, there are an infinity of inverses, and polyphase formulations help finding synthesis FBs.

A set of useful books (to me):

  • $\begingroup$ Thanks! It's awesome paper! I don't Know why the book of Crochiere "Multirate Digital Signal Processing" says only integer oversampling ratio.. $\endgroup$ – Stefano Jan 5 '16 at 23:09
  • $\begingroup$ 1st edition, page 325 where talks about comparision between polyphase and wola. $\endgroup$ – Stefano Jan 6 '16 at 10:22
  • $\begingroup$ I understand the chapter as "In this section [...] the polyphase structure is limited primarily to the critically sampled case where $M = K$ or to cases when $MI = K$, where $I$ is an integer". Sooner, they say that "This realization is most easily seen for the case of critically sampled filter banks where $M = K$. Designs for other choices of $M$ (or $K$) are not as straightforward as the critically sampled case". Primarily is important here. It does not mean it is impossible $\endgroup$ – Laurent Duval Jan 6 '16 at 19:35
  • $\begingroup$ Ok i didn't understand well. Thanks. I have another doubt .(, having M channels, N decimation factor and polyphase structure. In all documents, the analysis polyphase matrix is MxN. But Why? If the prototype filter H0 has length L, the matrix should have M x L/M, or not? Namely, for me each row of this matrix represents one polyphase component of length L/M. Where do i wrong? $\endgroup$ – Stefano Jan 6 '16 at 21:04
  • $\begingroup$ Polyphase behave like a subsampling of filter coefficients by $N$. So you have the subsequences $0, N, 2N...$, $1, N+1, 2N+1...$ up to $N-1,2N-1, ...$, hence $(N-1)-0+1$ polyphase component per filter. The polyphase size does not depend on the filter size, which is one of its main advantages. $\endgroup$ – Laurent Duval Jan 6 '16 at 21:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.