Perfect reconstruction biorthogonal multifilter banks

For compactly supported biorthogonal multiwavelets system with multiplicity r, we show that many new matrix biorthonormal multifilter banks (BMFs) can be constructed from the given matrix BMFs and vice versa. We also present an approach for constructing higher-order matrix BMFs from lower-order ones. If the original BMFs satisfy perfect reconstruction condition, then the new ones constructed using our method also satisfy perfect reconstruction condition. In addition, we also establish the relationship between the old BMFs and new ones when the two input vector sequences satisfy certain linear relations, which is important for application in signal processing.