Audio Signal Processing and Coding

6.6 COSINE MODULATED “PSEUDO QMF” M-BAND BANKS

A tree-structured cascade of two-channel prototypes is only one of several well-known methods available for realization of an M-band filter bank. Although the tree structures offer opportunities for optimization at each node and are conceptually simple, the potential for long delay and irregular channel responses is sometimes unappealing. As an alternative to the tree-structured architecture, cosine modulation of a lowpass prototype filter has been used since the early 1980s [Nuss81] [Roth83] [Chu85] [Mass85] [Cox86] to realize parallel M-channel filter banks with nearly perfect reconstruction. Because they do not achieve perfect reconstruction, these filter banks are known collectively as “pseudo QMF,” and they are characterized by several attractive properties:

• Constrained design; single FIR prototype filter
• Uniform, linear phase channel responses
• Overall linear phase, hence constant group delay
• Low complexity, i.e., one filter plus modulation
• Amenable to fast block algorithms
• Critical sampling.

In the pseudo QMF (PQMF) bank derivation phase distortion is completely eliminated from the overall transfer function, Eq. (6.5), by forcing the analysis and synthesis filters to satisfy the mirror image condition

Moreover, adjacent channel aliasing is cancelled by establishing precise relationships between the analysis and synthesis filters, ...