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Recent developments in multidimensional multirate systems

Chen, Tsuhan and Vaidyanathan, P. P. (1993) Recent developments in multidimensional multirate systems. IEEE Transactions on Circuits and Systems for Video Technology, 3 (2). pp. 116-137. ISSN 1051-8215. doi:10.1109/76.212718.

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Multidimensional (MD) multirate systems, which find applications in the coding and compression of image and video data, have recently attracted much attention. The basic building blocks in an MD multirate system are the decimation matrix M, the expansion matrix L, and MD digital filters. With D denoting the number of dimensions, M and L are D×D nonsingular integer matrices. When these matrices are diagonal, most of the one-dimensional (1-D) multirate results can be extended automatically, using separable approaches (i.e., separable operations in each dimension). Separable approaches are commonly used in practice due to their low complexity in implementation. However, nonseparable operations, with respect to nondiagonal decimation and expansion matrices, often provide more flexibility and better performance. Several applications, such as the conversion between progressive and interlaced video signals, actually require the use of nonseparable operations. For the nonseparable case, extensions of 1-D results to the MD case are nontrivial. Some of these extensions, e.g., polyphase decomposition and maximally decimated perfect reconstruction systems, have already been successfully accomplished by some authors. However, there exist several 1-D results in multirate processing for which the MD extensions are even more difficult. In this paper, we will introduce some recent developments in these extensions. Some important results are: the design of nonseparable MD decimation / interpolation filters derived from 1-D filters, the generalized pseudocirculant property of alias-free maximally decimated filter banks, the commutativity of MD decimators and expanders, and applications in the efficient polyphase implementation of MD rational decimation systems. We will also introduce several other results of theoretical importance.

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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 1993 IEEE. Reprinted with permission. Manuscript received December 24, 1991; revised September 11, 1992 and December 8, 1992. This work was supported in part by the National Science Foundation under Grants MIP 8604456 and MIP 8919196 and by matching funds from Tektronix, Inc., Hughes Aircraft Co., and Rockwell International. Paper was recommended by Associate Editor Yrjö Neuvo.
Subject Keywords:filtering and prediction theory; multidimensional digital filters; signal processing
Issue or Number:2
Record Number:CaltechAUTHORS:CHEieeetcsvt93
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9936
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Deposited On:27 Mar 2008
Last Modified:13 Apr 2022 17:12

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