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Biorthogonal partners and applications

Vaidyanathan, P. P. and Vrcelj, Bojan (2001) Biorthogonal partners and applications. IEEE Transactions on Signal Processing, 49 (5). pp. 1013-1027. ISSN 1053-587X. 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.


Item Type:Article
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
Record Number:CaltechAUTHORS:VAIieeetsp00
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp00
Alternative URL:http://dx.doi.org/10.1109/78.917805
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:02 Oct 2019 23:53

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