Pseudo-QMF Cosine Modulation Filter Bank
Section 11.3.5 introduced two-channel quadrature mirror filter banks (QMF). QMFs were shown to provide a particular class of perfect reconstruction filter banks. We found, however, that the quadrature mirror constraint on the analysis filters,
![]() |
(12.97) |
was rather severe in that linear-phase FIR implementations only exist in the two-tap case
![$ H_k(z) = h_{0k}+h_{1k}z^{-1}$](http://www.dsprelated.com/josimages_new/sasp2/img2248.png)
![$ k=0,1$](http://www.dsprelated.com/josimages_new/sasp2/img2249.png)
![$ N$](http://www.dsprelated.com/josimages_new/sasp2/img61.png)
![$ N$](http://www.dsprelated.com/josimages_new/sasp2/img61.png)
The Pseudo-QMF (PQMF) filter bank is a ``near perfect
reconstruction'' filter bank in which aliasing cancellation occurs
only between adjacent bands [194,287]. The PQMF
filters commonly used in perceptual audio coders employ bandpass
filters with stop-band attenuation near
dB, so the neglected
bands (which alias freely) are not significant. An outline of the
design procedure is as follows:
- Design a lowpass prototype window,
, with length
,
- The lowpass design is
constrained to give aliasing cancellation in neighboring subbands:
- The filter bank analysis filters
are cosine modulations of
:
(12.98)
, where the phases are restricted according to
(12.99)
again for aliasing cancellation. - Since it is an orthogonal filter bank by construction,
the synthesis filters are simply the time-reverse of the analysis filters:
(12.100)
![$ N=32$](http://www.dsprelated.com/josimages_new/sasp2/img2257.png)
![$ M=512$](http://www.dsprelated.com/josimages_new/sasp2/img2258.png)
![$ L=8$](http://www.dsprelated.com/josimages_new/sasp2/img2259.png)
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Perfect Reconstruction Cosine Modulated Filter Banks
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Polyphase Analysis of Portnoff STFT