On uncertainty principle of the local polynomial Fourier transform
Date of Issue2012
School of Electrical and Electronic Engineering
In this article, a comprehensive study on uncertainty principle of the local polynomial Fourier transform (LPFT) is presented. It shows that the uncertainty product of the LPFT of an arbitrary order is related to the parameters of the signal and the window function, in addition to the errors of estimating the polynomial coefficients. Important factors that affect resolutions of signal representation, such as the window width, the length of overlap between signal segments, order mismatch and estimation errors of polynomial coefficients, are discussed. The effects of minimizing computational complexities on signal representation by reducing the order of the transform and the overlap length between signal segments are also examined. In terms of the signal concentration, comparisons among the short-time Fourier transform, the Wigner-Ville distribution and the second order LPFT are presented. The LPFT is shown to be an excellent candidate providing better representations for time-varying signals.
DRNTU::Engineering::Electrical and electronic engineering
EURASIP journal on advances in signal processing
© 2012 Li et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.