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In this paper, we propose a design method of perfect reconstruction (PR) nonuniform filter banks. Filter banks are roughly separated into nonparaunitary and paraunitary ones. Paraunitary filter banks have some advantages: for example, the frequency responses of synthesis filters are identical to those of analysis filters. However, the severe constraint makes it difficult to design them and, especially in the nonuniform case, the design method becomes complex for some frequency-division cases. Thus, we concentrate on nonparaunitary filter banks and present a design method for nonuniform filter banks with arbitrary lengths and frequency divisions. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(10): 51–59 1997 [ABSTRACT FROM AUTHOR]

There are some applications that require oversampled filter banks, for example, adaptive signal processing using multirate filter banks. Little study was done, however, for such filter banks compared with maximally decimated ones. In this paper, we propose a design method for oversampled filter banks which satisfy the perfect reconstruction and linear phase properties. Moreover, we consider the design method for both orthogonal and biorthogonal ones. When the decimation ratio is not a divisor of the number of channels, we find it impossible for analysis and synthesis filters to have the same frequency responses by considering the mechanism of aliasing cancellation. In other words, biorthogonal filter banks can be designed under an arbitrary decimation ratio, while it is restricted to a divisor of the number of channels in the orthogonal case. We first derive the conditions for perfect reconstruction and linear phase for both biorthogonal and orthogonal ones. Then, we present the design method for both cases. Finally, some design examples are shown. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(10): 78–86, 1997 [ABSTRACT FROM AUTHOR]