Vaidyanathan, P. P. and Vrcelj, Bojan (2001) Biorthogonal partners and applications. IEEE Transactions on Signal Processing, 49 (5). pp. 1013-1027. ISSN 1053-587X. doi:10.1109/78.917805. https://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp00
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Abstract
Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications.
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| Additional Information: | © Copyright 2001 IEEE. Reprinted with permission. Manuscript received April 21, 2000; revised January 29, 2001. This work was supported in part by the Office of Naval Research under Grant N00014-99-1-1002 and by Microsoft Research, Redmond, WA. The associate editor coordinating the review of this paper and approving it for publication was Prof. Hideaki Sakai. | ||||||
| Subject Keywords: | channel bank filters, digital communication, digital filters, equalizers, filtering theory, interpolation, least squares approximations, signal resolution, transfer functions | ||||||
| Issue or Number: | 5 | ||||||
| DOI: | 10.1109/78.917805 | ||||||
| Record Number: | CaltechAUTHORS:VAIieeetsp00 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp00 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 8700 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Archive Administrator | ||||||
| Deposited On: | 06 Sep 2007 | ||||||
| Last Modified: | 08 Nov 2021 20:52 |
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