TY - JOUR
T1 - On the Positiveness of A Functional Symmetric Matrix Used in Digital Filter Design
AU - Wu, Yan
PY - 2004/10/1
Y1 - 2004/10/1
N2 - 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.
AB - 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.
KW - Digital Filter Design
KW - Functional Symmetric Matrix
UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/686
UR - https://doi.org/10.1142/S0218126604001787
U2 - 10.1142/S0218126604001787
DO - 10.1142/S0218126604001787
M3 - Article
VL - 13
JO - Journal of Circuits, Systems, and Computers
JF - Journal of Circuits, Systems, and Computers
ER -