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Multidimensional multirate filters and filter banks derived from one-dimensional filters

Chen, Tsuhan and Vaidyanathan, P. P. (1993) Multidimensional multirate filters and filter banks derived from one-dimensional filters. IEEE Transactions on Signal Processing, 41 (5). pp. 1749-1765. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:CHEieeetsp93c

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Abstract

A method by which every multidimensional (M-D) filter with an arbitrary parallelepiped-shaped passband support can be designed and implemented efficiently is presented. It is shown that all such filters can be designed starting from an appropriate one-dimensional prototype filter and performing a simple transformation. With D denoting the number of dimensions, the complexity of design and implementation of the M-D filter are reduced from O(ND) to O(N). Using the polyphase technique, an implementation with complexity of only 2N is obtained in the two-dimensional. Even though the filters designed are in general nonseparable, they have separable polyphase components. One special application of this method is in M-D multirate signal processing, where filters with parallelepiped-shaped passbands are used in decimation, interpolation, and filter banks. Some generalizations and other applications of this approach, including M-D uniform discrete Fourier transform (DFT) quadrature mirror filter banks that achieve perfect reconstruction, are studied. Several design example are given.


Item Type:Article
Additional Information:© Copyright 1993 IEEE. Reprinted with permission. Manuscript received February 9, 1991; revised July 21, 1992. The associate editor coordinating the review of this paper and approving it for publication was Prof. Faye Boudreaux-Bartels. This work was supported in part by the National Science Foundation Grants MIP 8604456, MIP 8919196, and by matching funds from Tektronix, Inc., Hughes Aircraft Company, and Rockwell International.
Subject Keywords:fast Fourier transforms; multidimensional digital filters; signal processing
Record Number:CaltechAUTHORS:CHEieeetsp93c
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHEieeetsp93c
Alternative URL:http://dx.doi.org/10.1109/78.215297
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9915
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:26 Mar 2008
Last Modified:26 Dec 2012 09:54

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