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Cyclic LTI systems in digital signal processing

Vaidyanathan, P. P. and Kiraç, Ahmet (1999) Cyclic LTI systems in digital signal processing. IEEE Transactions on Signal Processing, 47 (2). pp. 433-447. ISSN 1053-587X http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp99

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Abstract

Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L. In such cases, the frequency domain is defined as a uniform discrete grid (as in L-point DFT). This offers more freedom in theoretical as well as design aspects. While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, especially from the viewpoint of linear system theory, has not been studied in the past. In this paper, we introduce the fundamentals of cyclic multirate systems and filter banks, presenting several important differences between the cyclic and noncyclic cases. Cyclic systems with allpass and paraunitary properties are studied. The paraunitary interpolation problem is introduced, and it is shown that the interpolation does not always succeed. State-space descriptions of cyclic LTI systems are introduced, and the notions of reachability and observability of state equations are revisited. It is shown that unlike in traditional linear systems, these two notions are not related to the system minimality in a simple way. Throughout the paper, a number of open problems are pointed out from the perspective of the signal processor as well as the system theorist.


Item Type:Article
Additional Information:© Copyright 1999 IEEE. Reprinted with permission. Manuscript received November 13, 1997; revised August 6, 1998. This work supported in part by the Office of Naval Research under Grant N00014-93-1-0231 and Tektronix, Inc. The associate editor coordinating the review of this paper and approving it for publication was Dr. Sergios Theodoridis.
Subject Keywords:Cyclic systems, cyclic filterbanks, cyclic wavelets
Record Number:CaltechAUTHORS:VAIieeetsp99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp99
Alternative URL:http://dx.doi.org/10.1109/78.740127
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6658
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:16 Dec 2006
Last Modified:26 Dec 2012 09:23

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