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,
was rather severe in that linear-phase FIR implementations only exist in the two-tap case , . In addition to relaxing this constraint, we need to be able to design an -channel filter bank for any .
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
, where the phases are restricted according to
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:
Perfect Reconstruction Cosine Modulated Filter Banks
Polyphase Analysis of Portnoff STFT