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The role of the discrete-time Kalman-Yakubovitch-Popov lemma in designing statistically optimum FIR orthonormal filter banks

Tuqan, Jamal and Vaidyanathan, P. P. (1998) The role of the discrete-time Kalman-Yakubovitch-Popov lemma in designing statistically optimum FIR orthonormal filter banks. In: IEEE International Symposium on Circuits and Systems (ISCAS '98), Monterey, CA. Vol.5. IEEE , Piscataway, NJ, pp. 122-125. ISBN 0780344553.

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We introduce a new approach to design FIR energy compaction filters of arbitrary order N. The optimization of such filters is important due to their close connection to the design of an M-channel orthonormal filter bank adapted to the input signal statistics. The novel procedure finds the optimum product filter Fopt(Z)=H opt(Z)Hopt(Z^-1) corresponding to the compaction filter Hopt(z). The idea is to express F(z) as D(z)+D(z^-1) and reformulate the compaction problem in terms of the state space realization of the causal function D(z). For a fixed input power spectrum, the resulting filter Fopt(z) is guaranteed to be a global optimum due to the convexity of the new formulation. The new design method can be solved quite efficiently and with great accuracy using recently developed interior point methods and is extremely general in the sense that it works for any chosen M and any arbitrary filter length N. Finally, obtaining Hopt(z) from F opt(z) does not require an additional spectral factorization step. The minimum phase spectral factor can be obtained automatically by relating the state space realization of Dopt(z) to that of H opt(z).

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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 1998 IEEE. Reprinted with permission. Publication Date: 31 May-3 June 1998. This work is supported in parts by the NSF grant 0703755 and Tektronix. Inc.
Subject Keywords:FIR filters; Kalman filters; discrete time filters; filtering theory; state-space methods; causal function; convexity; discrete-time Kalman-Yakubovitch-Popov lemma; energy compaction filters; filter length; fixed input power; input signal statistics; interior point methods; minimum phase spectral factor; optimum product filter; state space realization; statistically optimum FIR orthonormal filter banks
Record Number:CaltechAUTHORS:TUQiscas98b
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ID Code:10785
Deposited On:10 Jun 2008
Last Modified:08 Nov 2021 21:11

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