Filter bank design based on time domain aliasing cancellation with non-identical windows

A new method of designing perfect reconstruction filter banks using analysis and synthesis windows that are not identical is presented. The filter bank design method is based on time domain aliasing cancellation (TDAC) introduced by Princen and Bradley (1986). In this proof, a generalisation of window design is achieved by removing the restrictions on window shapes. The present authors show that by utilising a post-processing amplitude equalisation window, perfect reconstruction can be maintained through control of aliasing cancellation alone. This allows a new degree of freedom for control of window shape and frequency domain selectivity. They also present an algebraic derivation of the perfect reconstruction requirements that allows the equalisation window to be merged into the synthesis process. Merging the two windows results in a perfect reconstruction filter bank that has non identical analysis and synthesis windows