Polynomial Wigner-Ville distributions

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Polynomial Wigner-Ville distributions

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Title: Polynomial Wigner-Ville distributions
Author: Benidir, Messaoud; Boashash, Boualem
Abstract: We propose a representation of the derivitive (phi) ' of any general polynomial (phi) of degree N in terms of Q equals N + 1 given parameters: t1,...,tQ. This representation allows us to express the derivative as a linear comination of q arbitrary ratios of [(phi) (t + (tau) (kappa )) - (phi) (t - (tau) (kappa ))]/(tau) (kappa ) calculated at q arbitrary points (tau) 1,...,(tau) q, where q denotes the integer part of (N + 1)/2. The coefficients appearing in this decomposition are independent of the polynomial coefficients. As an application, we give a formula that allows us to compute (phi) '(t) without using the coefficients of the polynomial (phi) (t) and establish a property of the polynomial Wigner-Ville distribution.
Description: This paper presents rigorous mathematical proofs of previous results presented in earlier papers for PTFDs. (The most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia., and then continuously updated).
URI: http://hdl.handle.net/10576/10709
Date: 1995-07

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