Design of an Optimal Piece-Wise Spline Wigner-Ville Distribution for TFD Performance Evaluation and Comparison

Mohammad Al-Sa'd; Boualem Boashash; Moncef Gabbouj

doi:10.1109/TSP.2021.3089291

Design of an Optimal Piece-Wise Spline Wigner-Ville Distribution for TFD Performance Evaluation and Comparison

Mohammad Al-Sa'd^*
, Boualem Boashash
, Moncef Gabbouj

^*Corresponding author for this work

Computing Sciences

Research output: Contribution to journal › Article › Scientific › peer-review

45 Citations (Scopus)

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Abstract

This paper proposes a new performance evaluation process for time-frequency distributions (TFD) by designing a reference optimal TFD and novel accuracy and resolution measures. The motivation comes from the need for a TFD performance evaluation method that is objective, capable of quantifying the TFD accuracy and resolution, can determine the performance difference among different TFDs, and suitable for signals with an arbitrary number of components, instantaneous frequency and amplitude. We formulate the proposed optimal TFD, namely the piece-wise spline Wigner-Ville distribution (PW-WVD), by decomposing a standard non-stationary signal model using piece-wise linear frequency modulated (LFM) basis and by exploiting the Wigner-Ville distribution optimality for LFM signals. We compare the designed PW-WVD to conventional optimal TFDs and show that the former is more suitable to serve as a reference for TFD performance evaluation. Using the PW-WVD we derive TFD accuracy and resolution measures, compare them to conventional approaches, and analyze their sensitivity to form a TFD selection criteria. We evaluate the accuracy and resolution of twelve different TFDs and develop precise TFD selection strategies with or without prior information on the signal parameters. Results indicate that the compact kernel distribution is the best performing TFD given no prior information on the signal parameters and different TFDs must be selected upon the availability of prior information.

Original language	English
Pages (from-to)	3963-3976
Number of pages	14
Journal	IEEE Transactions on Signal Processing
Volume	69
DOIs	https://doi.org/10.1109/TSP.2021.3089291
Publication status	Published - 2021
Publication type	A1 Journal article-refereed

Funding

Manuscript received September 26, 2020; revised March 15, 2021 and June 1, 2021; accepted June 9, 2021. Date of publication June 15, 2021; date of current version July 27, 2021. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Lorenzo Galleani. The work was supported in part by NSF IUCRC CVDI AMALIA project funded by Business Finland, and in part by Stroke-Data project funded by Haltian and the Office of the Provost. (Corresponding author: Mohammad Al-Sa’d.) Mohammad Al-Sa’d and Moncef Gabbouj are with the Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland (e-mail: [email protected]; [email protected]).

Keywords

Multi-component signals
performance evaluation
piece-wise LFM signals
time-frequency distribution
time-frequency measures
time-frequency representation

Publication forum classification

Publication forum level 3

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

Access to Document

10.1109/TSP.2021.3089291Licence: CC BY-NC-ND

Design_of_an_Optimal_Piece-Wise_Spline_Wigner-Ville_Distribution_for_TFD_Performance_Evaluation_and_ComparisonFinal published version, 4.15 MBLicence: CC BY-NC-ND

http://urn.fi/URN:NBN:fi:tuni-202109277282Licence: CC BY-NC-ND

Cite this

@article{932d5e4a36904ea799ecb20d719103e2,

title = "Design of an Optimal Piece-Wise Spline Wigner-Ville Distribution for TFD Performance Evaluation and Comparison",

abstract = "This paper proposes a new performance evaluation process for time-frequency distributions (TFD) by designing a reference optimal TFD and novel accuracy and resolution measures. The motivation comes from the need for a TFD performance evaluation method that is objective, capable of quantifying the TFD accuracy and resolution, can determine the performance difference among different TFDs, and suitable for signals with an arbitrary number of components, instantaneous frequency and amplitude. We formulate the proposed optimal TFD, namely the piece-wise spline Wigner-Ville distribution (PW-WVD), by decomposing a standard non-stationary signal model using piece-wise linear frequency modulated (LFM) basis and by exploiting the Wigner-Ville distribution optimality for LFM signals. We compare the designed PW-WVD to conventional optimal TFDs and show that the former is more suitable to serve as a reference for TFD performance evaluation. Using the PW-WVD we derive TFD accuracy and resolution measures, compare them to conventional approaches, and analyze their sensitivity to form a TFD selection criteria. We evaluate the accuracy and resolution of twelve different TFDs and develop precise TFD selection strategies with or without prior information on the signal parameters. Results indicate that the compact kernel distribution is the best performing TFD given no prior information on the signal parameters and different TFDs must be selected upon the availability of prior information. ",

keywords = "Multi-component signals, performance evaluation, piece-wise LFM signals, time-frequency distribution, time-frequency measures, time-frequency representation",

author = "Mohammad Al-Sa'd and Boualem Boashash and Moncef Gabbouj",

note = "Funding Information: Manuscript received September 26, 2020; revised March 15, 2021 and June 1, 2021; accepted June 9, 2021. Date of publication June 15, 2021; date of current version July 27, 2021. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Lorenzo Galleani. The work was supported in part by NSF IUCRC CVDI AMALIA project funded by Business Finland, and in part by Stroke-Data project funded by Haltian and the Office of the Provost. (Corresponding author: Mohammad Al-Sa{\textquoteright}d.) Mohammad Al-Sa{\textquoteright}d and Moncef Gabbouj are with the Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland (e-mail: [email protected]; [email protected]). Publisher Copyright: {\textcopyright} 1991-2012 IEEE.",

year = "2021",

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language = "English",

volume = "69",

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journal = "IEEE Transactions on Signal Processing",

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AU - Al-Sa'd, Mohammad

AU - Boashash, Boualem

AU - Gabbouj, Moncef

N1 - Funding Information: Manuscript received September 26, 2020; revised March 15, 2021 and June 1, 2021; accepted June 9, 2021. Date of publication June 15, 2021; date of current version July 27, 2021. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Lorenzo Galleani. The work was supported in part by NSF IUCRC CVDI AMALIA project funded by Business Finland, and in part by Stroke-Data project funded by Haltian and the Office of the Provost. (Corresponding author: Mohammad Al-Sa’d.) Mohammad Al-Sa’d and Moncef Gabbouj are with the Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland (e-mail: [email protected]; [email protected]). Publisher Copyright: © 1991-2012 IEEE.

PY - 2021

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N2 - This paper proposes a new performance evaluation process for time-frequency distributions (TFD) by designing a reference optimal TFD and novel accuracy and resolution measures. The motivation comes from the need for a TFD performance evaluation method that is objective, capable of quantifying the TFD accuracy and resolution, can determine the performance difference among different TFDs, and suitable for signals with an arbitrary number of components, instantaneous frequency and amplitude. We formulate the proposed optimal TFD, namely the piece-wise spline Wigner-Ville distribution (PW-WVD), by decomposing a standard non-stationary signal model using piece-wise linear frequency modulated (LFM) basis and by exploiting the Wigner-Ville distribution optimality for LFM signals. We compare the designed PW-WVD to conventional optimal TFDs and show that the former is more suitable to serve as a reference for TFD performance evaluation. Using the PW-WVD we derive TFD accuracy and resolution measures, compare them to conventional approaches, and analyze their sensitivity to form a TFD selection criteria. We evaluate the accuracy and resolution of twelve different TFDs and develop precise TFD selection strategies with or without prior information on the signal parameters. Results indicate that the compact kernel distribution is the best performing TFD given no prior information on the signal parameters and different TFDs must be selected upon the availability of prior information.

AB - This paper proposes a new performance evaluation process for time-frequency distributions (TFD) by designing a reference optimal TFD and novel accuracy and resolution measures. The motivation comes from the need for a TFD performance evaluation method that is objective, capable of quantifying the TFD accuracy and resolution, can determine the performance difference among different TFDs, and suitable for signals with an arbitrary number of components, instantaneous frequency and amplitude. We formulate the proposed optimal TFD, namely the piece-wise spline Wigner-Ville distribution (PW-WVD), by decomposing a standard non-stationary signal model using piece-wise linear frequency modulated (LFM) basis and by exploiting the Wigner-Ville distribution optimality for LFM signals. We compare the designed PW-WVD to conventional optimal TFDs and show that the former is more suitable to serve as a reference for TFD performance evaluation. Using the PW-WVD we derive TFD accuracy and resolution measures, compare them to conventional approaches, and analyze their sensitivity to form a TFD selection criteria. We evaluate the accuracy and resolution of twelve different TFDs and develop precise TFD selection strategies with or without prior information on the signal parameters. Results indicate that the compact kernel distribution is the best performing TFD given no prior information on the signal parameters and different TFDs must be selected upon the availability of prior information.

KW - Multi-component signals

KW - performance evaluation

KW - piece-wise LFM signals

KW - time-frequency distribution

KW - time-frequency measures

KW - time-frequency representation

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DO - 10.1109/TSP.2021.3089291

M3 - Article

AN - SCOPUS:85111977665

SN - 1053-587X

VL - 69

SP - 3963

EP - 3976

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

ER -

Design of an Optimal Piece-Wise Spline Wigner-Ville Distribution for TFD Performance Evaluation and Comparison

Abstract

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