A note on covariance-invariant digital filter design and autoregressive moving average spectrum analysis

Author

Kinkel, John F. ; Perl, Joseph ; Scharf, Louis L. ; Stubberud, Allen R.

Author_Institution

Irvine Avenue, Newport Beach, CA

Volume

27

Issue

2

fYear

1979

fDate

4/1/1979 12:00:00 AM

Firstpage

200

Lastpage

202

Abstract

Consider an autoregressive-moving average (ARMA) discrete-time sequence ${x_{k}}$ with covariance sequence ${R_{k}}$ . Equations are given for the solution of the AR coefficients ${a_{k}}\\min{1}\\max {n}$ in terms of the covariances ${R_{k}}\\min{0}\\max {2n-1}$ , and subsequent solution for the MA coefficients ${b_{k}}\\min{1}\\max {n}$ in terms of the AR coefficients and the covariances ${R_{k}}\\min{0}\\max {n-1}$ . The results are derived and presented somewhat differently than usual to complement the results of [1] for the synthesis of covariance-invariant digital filters. In the context of spectrum analysis, the results provide a means of performing ARMA spectrum analysis on data that arise as sampled data from a rational continuous-time process [2]. An important result, originally derived in [2], shows that the ARMA spectrum can be obtained without actually solving the nonlinear factorization problem for the MA coefficients.

Keywords

Acoustic pulses; Covariance matrix; Data analysis; Digital filters; Equations; Performance analysis; Probability; Speech analysis; Statistics; Transfer functions;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/TASSP.1979.1163220

Filename

1163220