On the Positiveness of A Functional Symmetric Matrix Used in Digital Filter Design
Journal of Circuits, Systems, and Computers
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.
"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 source: https://www.worldscientific.com/doi/abs/10.1142/S0218126604001787