Reconstruction of a positive definite Toeplitz matrix from its sequence of minimum eigenvalues

Author

Clements, Mark A. ; Isabelle, Steven H.

Author_Institution

Sch. of Electr. Eng., Georgia Inst. of Technol., Atlanta, GA, USA

Volume

36

Issue

11

fYear

1988

fDate

11/1/1988 12:00:00 AM

Firstpage

1784

Lastpage

1786

Abstract

It is shown that a positive definite symmetric Toeplitz matrix of rank p+1 can be represented uniquely by the minimum eigenvalues of itself and its p submatrices, along with a sign bit for each eigenvalue. The application of such a procedure allows specification of linear prediction coding (LPC) spectra by an alternate set of parameters. It also enables extension of an autocorrelation sequence using a nonstandard criterion. A number of parallels are made between these parameters and the LPC mean-square error values for successively higher-order systems. An application involving maximum entropy spectral estimation under a nonstandard set of constraints is presented

Keywords

eigenvalues and eigenfunctions; encoding; matrix algebra; spectral analysis; autocorrelation sequence; linear prediction coding; maximum entropy spectral estimation; minimum eigenvalues; nonstandard criterion; positive definite Toeplitz matrix; sign bit; submatrices; successively higher-order systems; Acoustics; Autocorrelation; Eigenvalues and eigenfunctions; Entropy; Filters; Linear predictive coding; Polynomials; Quantization; Speech processing; Symmetric matrices;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.9017

Filename

9017