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ON THE POSITIVENESS OF A FUNCTIONAL SYMMETRIC MATRIX USED IN DIGITAL FILTER DESIGN
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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