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This paper describes an efficient structure for generalized lapped orthogonal transforms (GenLOT) for finite-duration sequences, which we expect to be used for subband image coding. When linear convolution is carried out on the finite-duration sequences and filter, the number of points in the output signal increases. Therefore, the linear convolution is not desirable in subband image coding. In order to solve this problem, the convolution is carried out after the finite-duration sequences are symmetrically and periodically extended (symmetric extension method). This method is superior to circular convolution because the former method causes less distortion at the signal boundaries. In the GenLOT structure proposed in this paper, the symmetric extension can be realized without redundant operations due to signal extension and, furthermore, with fast implementation. This structure is considered to be a generalization of the lapped orthogonal transform (LOT) for finite-duration sequences. In addition, its application to the M-band discrete-time wavelet transform (DTWT) will be described. Finally, it will be shown that an efficient structure for finite-duration sequences can be realized in the M-band DTWT. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(10): 39–50, 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]