A note on the evaluation of complex integrals using filtering interpretations

Author

Dugré, J.P. ; Jury, E.I.

Author_Institution

University of Rhode Island, Kingston, RI

Volume

30

Issue

5

fYear

1982

fDate

10/1/1982 12:00:00 AM

Firstpage

804

Lastpage

807

Abstract

The evaluation of complex integrals of the form $r_{k} = {1 \\over 2{\\pi}j} \\oint H(z) H(z^{-1}) z^{k} {dz \\over z}$ for all $k$ is frequently required in control, communications, and digital filtering problems. The major drawback of all existing methods is that the evaluation of the integral has to be preceded or followed by a check of the stability of the transfer function $H(z)$ to ensure that $\\{ r_{k}\\} {-\\infty \\atop +\\infty}$ is a true correlation sequence. In this correspondence we modify the method proposed in [1] to yield a simple linear algorithm that does not require a separate cheek for the stability of $H(z)$ . The filtering interpretations proposed in [1] are extended to the evaluation of more general complex integrals with integrands of the form $H(z) G(z^{-1})$ . Finally, an algorithm using the Levinson recursions is presented as a fast method to generate correlation sequences in the ARMA case.

Keywords

Adaptive filters; Circuits; Delay estimation; Digital filters; Filtering theory; Least squares approximation; Nonlinear filters; Signal processing algorithms; Smoothing methods; Speech processing;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/TASSP.1982.1163957

Filename

1163957