Boundary filter design for biorthogonal filter banks

In order for filter banks to be able to process finite length input signals, appropriate modifications must be made to either the input signal (via signal extension techniques) or to the filter bank itself (boundary filters). This paper shows how to choose appropriate boundary filters for the analysis portion of any filter bank. The boundary filters can be chosen to satisfy any number of criteria, such as frequency selectivity or number of vanishing moments, and are only required to be linearly independent of the original filter bank filters. The synthesis filter bank is found by calculating the dual of the analysis bank, which is the same as finding the inverse. This results in a biorthogonal, perfect reconstruction filter bank.