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.
Recommended Citation
Wu, Yan.
2004.
"On the Positiveness of A Functional Symmetric Matrix Used in Digital Filter Design."
Journal of Circuits, Systems, and Computers, 13 (5): 1105-1110.
doi: 10.1142/S0218126604001787
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/686
