### Perfect Reconstruction Cosine Modulated Filter Banks

By changing the phases , the pseudo-QMF filter bank can yield perfect reconstruction:

 (12.101)

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:

 (12.102)

However, the length of the filters can be any even multiple of :

 (12.103)

The parameter is called the overlapping factor. These filter banks are also referred to as extended lapped transforms, when [159].

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