Polynomial Wigner-Ville distributions

Messaoud Benidir; Boualem Boashash

doi:10.1117/12.211426

7 June 1995 Polynomial Wigner-Ville distributions

Messaoud Benidir, Boualem Boashash

Proceedings Volume 2563, Advanced Signal Processing Algorithms; (1995) https://doi.org/10.1117/12.211426
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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,...,t_Q. 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.

Citation Download Citation

Messaoud Benidir and Boualem Boashash "Polynomial Wigner-Ville distributions", Proc. SPIE 2563, Advanced Signal Processing Algorithms, (7 June 1995); https://doi.org/10.1117/12.211426

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