Perfect Reconstruction Cosine Modulated Filter BanksBy changing the phases , the pseudo-QMF filter bank can yield perfect reconstruction:
where is the length of the polyphase filter ( ). If , then this is the oddly stacked Princen-Bradley filter bank and the analysis filters are related by cosine modulations of the lowpass prototype:
However, the length of the filters can be any even multiple of :
The parameter is called the overlapping factor. These filter banks are also referred to as extended lapped transforms, when .
MPEG Layer III Filter Bank
Pseudo-QMF Cosine Modulation Filter Bank