Robust relative stability of time-invariant and time-varying lattice filters

S. Dasgupta; Minyue Fu; C. Schwarz

doi:10.1109/CDC.1996.573668

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Conference proceeding

Robust relative stability of time-invariant and time-varying lattice filters

S. Dasgupta, Minyue Fu and C. Schwarz

Proceedings of 35th IEEE Conference on Decision and Control, Vol.3, pp.3341-3346 vol.3

1996

DOI: 10.1109/CDC.1996.573668

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Abstract

We consider the relative stability of time invariant and time varying unnormalized lattice filters. First, we consider a set of lattice filters whose reflection parameters /spl alpha//sub i/, obey |/spl alpha//sub i/|/spl les//spl delta//sub i/, and provide necessary and sufficient conditions on the /spl delta//sub i/ that guarantee that each time invariant Lattice in the set has poles inside a circle of prescribed radius 1//spl rho/<1, i.e. they are relatively stable with degree of stability in /spl rho/. We also show that the relative stability of the whole family is equivalent to the relative stability of a single filter obtained by fixing each /spl alpha//sub i/ to /spl delta//sub i/, and can be checked with only the real poles of this filter. Counterexamples are given to show that a number of properties that hold for stability of LTI lattices do not apply to relative stability verification. Second, we give a diagonal Lyapunov matrix that is useful in checking the above pole condition. Finally, we consider the time varying problem where the reflection coefficients vary in a region where the frozen transfer functions have poles with magnitude less than 1//spl rho/, and provide bounds on their rate of variations that ensure that the zero input state solution of the time varying lattice decays exponentially at a rate faster than 1//spl rho/'>1//spl rho/.

Cities and towns

Ear

Lattices

Nonlinear filters

Poles and zeros

Reflection

Robust stability

Speech coding

Sufficient conditions

Transfer functions

Details

Title: Subtitle: Robust relative stability of time-invariant and time-varying lattice filters
Creators: S. Dasgupta - University of Iowa
Minyue Fu - University of Newcastle Australia
C. Schwarz - University of Iowa
Resource Type: Conference proceeding
Publication Details: Proceedings of 35th IEEE Conference on Decision and Control, Vol.3, pp.3341-3346 vol.3
Publisher: IEEE
DOI: 10.1109/CDC.1996.573668
ISSN: 0191-2216
Language: English
Date published: 1996
Academic Unit: Iowa Technology Institute; Driving Safety Research Institute
Record Identifier: 9984627295402771

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