Title

On the Positiveness of A Functional Symmetric Matrix Used in Digital Filter Design

Document Type

Article

Publication Date

10-2004

Publication Title

Journal of Circuits, Systems, and Computers

DOI

10.1142/S0218126604001787

ISSN

1793-6454

Abstract

This paper gives a simple proof for the positiveness of two important symmetric Toeplitz matrices used in communication and signal processing. It utilizes the shifting property of a so-called Uniformly Band-Restricted (UBR) function, which is the generating function for a generic functional symmetric matrix. It is shown that the functional symmetric matrix is positive definite if the UBR function is evaluated at a sequence of distinct real numbers.

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