A direct design framework for a class of oversampled perfect reconstruction filter banks

A novel framework for the design of oversampled perfect reconstruction filter banks in which all analysis and synthesis filters have the length of twice the downsampling factor is presented. It is shown that given a set of analysis filters, using only simple matrix operations, we can obtain the corresponding synthesis filters which yield perfect reconstruction. In the proposed approach, it is not necessary to employ any iterative optimization technique in order to obtain the synthesis filters. The analysis is performed based solely on observations in a linear vector space. Some design examples are provided and open problems are stated.