On the LTI properties of adaptive feedforward systems with tap delay-line regressors

Author

Bayard, David S.

Author_Institution

Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA

Volume

47

Issue

5

fYear

1999

fDate

5/1/1999 12:00:00 AM

Firstpage

1288

Lastpage

1296

Abstract

It is shown that an adaptive system whose regressor is formed by tap delay-line (TDL) filtering of a multitone sinusoidal signal is representable as a parallel connection of a linear time-invariant (LTI) block and a linear time-varying (LTV) block. A norm-bound (induced 2-norm) is computed explicitly on the LTV block and is shown to decrease as N^-1, where N is the number of taps. Hence, the adaptive system becomes LTI in the limit as the number of taps goes to infinity. In the more realistic case where the number of taps N is finite, the new “LTI plus norm-bounded perturbation” representation renders, for the first time, the adaptive system analyzable by standard robust control methods

Keywords

adaptive filters; adaptive signal processing; delay lines; feedforward; filtering theory; perturbation techniques; robust control; signal representation; LTI properties; LTV block; adaptive feedforward systems; adaptive system; linear time-invariant block; linear time-varying block; multitone sinusoidal signal representation; norm-bound; norm-bounded perturbation; parallel connection; standard robust control methods; tap delay-line filtering; tap delay-line regressors; Adaptive control; Adaptive filters; Adaptive systems; Delay; Feedforward systems; Filtering; H infinity control; Nonlinear filters; Programmable control; Time varying systems;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.757216

Filename

757216