Time-Frequency Distributions Based on Compact Support Kernels: Properties and Performance Evaluation

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Time-Frequency Distributions Based on Compact Support Kernels: Properties and Performance Evaluation

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Title: Time-Frequency Distributions Based on Compact Support Kernels: Properties and Performance Evaluation
Author: Abed, M; Belouchrani, A; Cheriet, M; Boashash, B
Abstract: This paper presents two new time-frequency distributions (TFDs) based on kernels with compact support (KCS) namely the separable (CB) (SCB) and the polynomial CB (PCB) TFDs. The implementation of this family of TFDs follows the method developed for the Cheriet-Belouchrani (CB) TFD. The mathematical properties of these three TFDs are analyzed and their performance is compared to the best classical quadratic TFDs using several tests on multi-component signals with linear and nonlinear frequency modulation (FM) components including the noise effects. Instead of relying solely on visual inspection of the time-frequency domain plots, comparisons include the time slices’ plots and the evaluation of the Boashash-Sucic’s normalized instantaneous resolution performance measure that permits to provide the optimized TFD using a specific methodology. In all presented examples, the KCS-TFDs show a significant interference rejection, with the component energy concentration around their respective instantaneous frequency laws yielding high resolution measure values.
Description: This paper presents new Compact-based kernel high-resolution TFDs which outperform other well known classical TFDs in terms of crossterms reduction while still achieving the best time-frequency resolution and then preserving high energy concentration around the components’ instantaneous frequencies. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, 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://dx.doi.org/10.1109/TSP.2012.2190065
http://hdl.handle.net/10576/10843
Date: 2012-06

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