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Orthonormal and biorthonormal filter banks as convolvers, and convolutional coding gain

Vaidyanathan, P. P. (1993) Orthonormal and biorthonormal filter banks as convolvers, and convolutional coding gain. IEEE Transactions on Signal Processing, 41 (6). pp. 2110-2130. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp93

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Abstract

Convolution theorems for filter bank transformers are introduced. Both uniform and nonuniform decimation ratios are considered, and orthonormal as well as biorthonormal cases are addressed. All the theorems are such that the original convolution reduces to a sum of shorter, decoupled convolutions in the subbands. That is, there is no need to have cross convolution between subbands. For the orthonormal case, expressions for optimal bit allocation and the optimized coding gain are derived. The contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum. With one of the convolved sequences taken to be the unit pulse function,,e coding gain expressions reduce to those for traditional subband and transform coding. The filter-bank convolver has about the same computational complexity as a traditional convolver, if the analysis bank has small complexity compared to the convolution itself.


Item Type:Article
Additional Information:© Copyright 1993 IEEE. Reprinted with permission. Manuscript received March 11, 1992; revised July 26, 1992. The associate editor coordinating the review of this paper and approving it for publication was Dr. S.D. Cabrera. This work was suppported in part by National Science Foundation Grant MIP 8919196 with matching funds from Rockwell Inc. and Tektronix, Inc. The author thanks T. Chen and S.-M. Phoong, graduate students at Caltech, for interesting discussions and their valuable comments on the paper. S.-M. Phoong also generated the numerical examples presented in Section V. S. Martucci of the Georgia Institute of Technology sent the author some references on DCT convolutions, including his preprint on that topic. One of the reviewers drew his attention to a recent doctoral dissertation [49], which addresses a number of issues on subband coding. When this paper was on its way to the press, Prof. M. Vetterli of Columbia University drew his attention to a very interesting monograph [50], which addresses convolution using DFT filter banks.
Record Number:CaltechAUTHORS:VAIieeetsp93
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp93
Alternative URL:http://dx.doi.org/10.1109/78.218140
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ID Code:7097
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Deposited On:08 Jan 2007
Last Modified:26 Dec 2012 09:29

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