Quadratic Tfd

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B. Boashash - One of the best experts on this subject based on the ideXlab platform.

  • Time Frequency Analysis - Chapter 3 - Theory of Quadratic Tfds
    Time Frequency Analysis, 2020
    Co-Authors: B. Boashash
    Abstract:

    This chapter discusses the theory of Quadratic time frequency distributions (Tfds). For a monocomponent linear FM signal, the Wigner-Ville distributions (WVD) is optimal for energy concentration about the instantaneous frequency (IF) and for unbiased estimation of the IF. If a signal has nonlinear frequency modulation or multiple components, the WVD suffers from inner artifacts or outer artifacts (cross-terms), respectively; in either case, some form of reduced interference Quadratic Tfd (RID) is to be preferred over the WVD. The design of RIDs is best undertaken by designing the desired kernel filter in the ambiguity domain, and using Fourier transforms to see the effects in the time-lag and time–frequency domains. To be a useful tool for practical applications, Quadratic Tfds are expected to be real, to satisfy the global and local energy requirements, and to resolve signal components while reflecting the components' IF laws through the peaks of their dominant ridges in the (t, f) plane.

  • Optimisation of the realisation of Quadratic discrete time-freqeuncy distributions as a Matlab toolbox
    2020
    Co-Authors: John M. O'toole, B. Boashash
    Abstract:

    An optimised time-frequency signal analysis software tool is presented here as a MATLAB toolbox. This toolbox is implemented using existing and novel methods for a specific class of Time-Frequency Distributions (Tfds) called Quadratic Tfds. This is first applied to a Tfd called the Wigner-Ville Distribution (WVD), as all other Quadratic Tfds can be represented as a smoothed (in both time and frequency) version of the WVD. This method is then extended to the general Quadratic Tfd case, where the complete implementation optimises both simulation speed and memory usage. Also some Quadratic Tfds can be represented in their direct form, such as the Spectrogram and Rihaczek distribution. The optimization of the implementation of these distributions is also examined.

  • ISSPA - Resolution analysis of the T-class time-frequency distributions
    2007 9th International Symposium on Signal Processing and Its Applications, 2020
    Co-Authors: L. Rankine, Mostefa Mesbah, B. Boashash
    Abstract:

    The T-class of time-frequency distributions (Tfds) is a newly proposed subclass of the general Quadratic Tfd class. The Tfds of this subclass are characterized by their time-lag kernels which are functions of time only. In this paper, we report the results of our investigation related to the time and frequency resolution of the T-class Tfds. It is shown, analytically, for the case of a linear chirp, that the frequency resolution is a function of both the smoothing parameter of the Tfd kernel and the rate of change in instantaneous frequency. The results are then illustrated with a number of synthetic examples.

  • Time Frequency Analysis - Chapter 2 - Heuristic Formulation of Time-Frequency Distributions
    Time Frequency Analysis, 2020
    Co-Authors: B. Boashash
    Abstract:

    This chapter discusses heuristic formulation of time frequency distributions (Tfd). The chapter examines a variety of ad hoc approaches to the problem, namely the Wigner-Ville distribution, localized forms of the Fourier Transform, filter banks, Page's instantaneous power spectrum, and related energy densities. The chapter also illustrates how all these distributions are related to the Wigner-Ville distribution. Constructing a Quadratic Tfd from the analytic associate of a given real signal, rather than from the signal itself, avoids spurious terms caused by interference between positive-frequency and negative-frequency components. Every Tfd derived heuristically is Quadratic in the signal; that is, if the signal is scaled by a factor k, the Tfd is scaled by a factor k 2. This is to be expected because each Tfd is related to some sort of energy density; the signal has been assumed to be an effort variable or a flow variable and power is proportional to the product of an effort variable and the corresponding flow variable, hence to the square of the effort variable.

  • Improved characterization of HRV signals based on instantaneous frequency features estimated from Quadratic time–frequency distributions with data-adapted kernels
    Biomedical Signal Processing and Control, 2014
    Co-Authors: Shiying Dong, Ghasem Azemi, B. Boashash
    Abstract:

    The analysis of heart rate variability (HRV) provides a non-invasive tool for assessing the autonomicregulation of cardiovascular system. Quadratic time–frequency distributions (Tfds) have been used toaccount for the non-stationarity of HRV signals, but their performance is affected by cross-terms. Thisstudy presents an improved type of Quadratic Tfd with a lag-independent kernel (LIK-Tfd) by introducinga new parameter defined as the minimal frequency distance among signal components. The resultingTfd with this LIK can effectively suppress the cross-terms while maintaining the time–frequency (TF)resolution needed for accurate characterization of HRV signals. Results of quantitative and qualitativetests on both simulated and real HRV signals show that the proposed LIK-Tfds outperform other Tfdscommonly used in HRV analysis. The findings of the study indicate that these LIK-Tfds provide morereliable TF characterization of HRV signals for extracting new instantaneous frequency (IF) based clinicallyrelated features. These IF based measurements shown to be important in detecting perinatal hypoxicinsult – a severe cause of morbidity and mortality in newborns.

Taoufik Ben-jabeur - One of the best experts on this subject based on the ideXlab platform.

  • EUSIPCO - Design of a new high-energy concentration kernel Quadratic Tfd for EEG spike signal
    2015 23rd European Signal Processing Conference (EUSIPCO), 2015
    Co-Authors: Taoufik Ben-jabeur, Abdullah Kadri
    Abstract:

    In this paper, the design of a novel high-energy concentration kernel Quadratic Tfd for EEG spike signal analysis is presented. Firstly, we show that the suppression of the negative frequency of the signal due of the use of Hilbert transform causes low Time-Frequency Distribution (Tfd) resolution in the very low frequency band. To remedy this artifact, a frequency shifting of the signal to the mid frequency band is used so that the negative and positive frequencies are taken into account in the time-frequency domain. This process enhances the Tfd resolution in the very low frequency band. Secondly, we derived a new separable kernel Tfd with a high auto-terms energy concentration based on the localization of the auto-terms and cross-terms of the EEG spike signal in the ambiguity domain. The proposed kernel uses only two parameters and offers high Tfd resolution compared to the existing ones.

  • Design of a new high-energy concentration kernel Quadratic Tfd for EEG spike signal
    2015 23rd European Signal Processing Conference (EUSIPCO), 2015
    Co-Authors: Taoufik Ben-jabeur, Abdullah Kadri
    Abstract:

    In this paper, the design of a novel high-energy concentration kernel Quadratic Tfd for EEG spike signal analysis is presented. Firstly, we show that the suppression of the negative frequency of the signal due of the use of Hilbert transform causes low Time-Frequency Distribution (Tfd) resolution in the very low frequency band. To remedy this artifact, a frequency shifting of the signal to the mid frequency band is used so that the negative and positive frequencies are taken into account in the time-frequency domain. This process enhances the Tfd resolution in the very low frequency band. Secondly, we derived a new separable kernel Tfd with a high auto-terms energy concentration based on the localization of the auto-terms and cross-terms of the EEG spike signal in the ambiguity domain. The proposed kernel uses only two parameters and offers high Tfd resolution compared to the existing ones.

  • Design of a high-resolution separable-kernel Quadratic Tfd for improving newborn health outcomes using fetal movement detection
    2012 11th International Conference on Information Science Signal Processing and their Applications (ISSPA), 2012
    Co-Authors: B. Boashash, Taoufik Ben-jabeur
    Abstract:

    Prior to birth, fetus health can be monitored by the variety and scale of its movements. In addition, at birth, EEG signals are recorded from at-risk newborns. Studies have shown that both fetal movements and newborn EEGs are non-stationary signals. This paper aims to represent both newborn EEG and fetal movement signals in a time-frequency domain using a specifically designed time-frequency distribution (Tfd) that is well adapted to these types of data for the purpose of analysis, detection and classification. The approach to design the Quadratic TfdS is based on relating separable-kernel TfdS to DSP spectral window and digital filter design. To reach this goal, we compared recently proposed Tfds such as the Modified B distribution, a separable Gaussian distribution and the B distribution. Then, an extension of the modified B distribution (MBD) is proposed, referred to as the extended separable-kernel MBD. This new Tfd uses a separable kernel based on an extension of the modified B kernel in both time and frequency domain with different windows for each domain. Simulation results are provided to compare the proposed Method with different Tfds and to assess its performance. The new Tfd is then first applied to real fetal movement data recorded using accelerometers.

  • ISSPA - Design of a high-resolution separable-kernel Quadratic Tfd for improving newborn health outcomes using fetal movement detection
    2012 11th International Conference on Information Science Signal Processing and their Applications (ISSPA), 2012
    Co-Authors: B. Boashash, Taoufik Ben-jabeur
    Abstract:

    Prior to birth, fetus health can be monitored by the variety and scale of its movements. In addition, at birth, EEG signals are recorded from at-risk newborns. Studies have shown that both fetal movements and newborn EEGs are non-stationary signals. This paper aims to represent both newborn EEG and fetal movement signals in a time-frequency domain using a specifically designed time-frequency distribution (Tfd) that is well adapted to these types of data for the purpose of analysis, detection and classification. The approach to design the Quadratic TfdS is based on relating separable-kernel TfdS to DSP spectral window and digital filter design. To reach this goal, we compared recently proposed Tfds such as the Modified B distribution, a separable Gaussian distribution and the B distribution. Then, an extension of the modified B distribution(MBD) is proposed, referred to as the extended separable-kernel MBD. This new Tfd uses a separable kernel based on an extension of the modified B kernel in both time and frequency domain with different windows for each domain. Simulation results are provided to compare the proposed Method with different Tfds and to assess its performance. The new Tfd is then first applied to real fetal movement data recorded using accelerometers.

Abdullah Kadri - One of the best experts on this subject based on the ideXlab platform.

  • EUSIPCO - Design of a new high-energy concentration kernel Quadratic Tfd for EEG spike signal
    2015 23rd European Signal Processing Conference (EUSIPCO), 2015
    Co-Authors: Taoufik Ben-jabeur, Abdullah Kadri
    Abstract:

    In this paper, the design of a novel high-energy concentration kernel Quadratic Tfd for EEG spike signal analysis is presented. Firstly, we show that the suppression of the negative frequency of the signal due of the use of Hilbert transform causes low Time-Frequency Distribution (Tfd) resolution in the very low frequency band. To remedy this artifact, a frequency shifting of the signal to the mid frequency band is used so that the negative and positive frequencies are taken into account in the time-frequency domain. This process enhances the Tfd resolution in the very low frequency band. Secondly, we derived a new separable kernel Tfd with a high auto-terms energy concentration based on the localization of the auto-terms and cross-terms of the EEG spike signal in the ambiguity domain. The proposed kernel uses only two parameters and offers high Tfd resolution compared to the existing ones.

  • Design of a new high-energy concentration kernel Quadratic Tfd for EEG spike signal
    2015 23rd European Signal Processing Conference (EUSIPCO), 2015
    Co-Authors: Taoufik Ben-jabeur, Abdullah Kadri
    Abstract:

    In this paper, the design of a novel high-energy concentration kernel Quadratic Tfd for EEG spike signal analysis is presented. Firstly, we show that the suppression of the negative frequency of the signal due of the use of Hilbert transform causes low Time-Frequency Distribution (Tfd) resolution in the very low frequency band. To remedy this artifact, a frequency shifting of the signal to the mid frequency band is used so that the negative and positive frequencies are taken into account in the time-frequency domain. This process enhances the Tfd resolution in the very low frequency band. Secondly, we derived a new separable kernel Tfd with a high auto-terms energy concentration based on the localization of the auto-terms and cross-terms of the EEG spike signal in the ambiguity domain. The proposed kernel uses only two parameters and offers high Tfd resolution compared to the existing ones.

Eric Moreau - One of the best experts on this subject based on the ideXlab platform.

  • nonorthogonal joint diagonalization zero diagonalization for source separation based on time frequency distributions
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: E M Fadaili, N T Moreau, Eric Moreau
    Abstract:

    This paper deals with the blind separation of instantaneous mixtures of source signals using time-frequency distributions (Tfds). We propose iterative algorithms to perform the nonorthogonal zero diagonalization and/or joint diagonalization of given sets of matrices. As an application, we show that the source separation can be realized by applying one of these algorithms to a set of spatial Quadratic Tfd matrices corresponding only to the so-called cross-source terms and/or to the so-called autosource terms. The determination of the above matrices to be jointly decomposed requires first an automatic selection procedure of useful time-frequency points. Regarding this last point, we also propose a new selection procedure and a modification of an existing one and provide a comparison with other existing ones. The nonorthogonal joint diagonalization and/or zero diagonalization algorithm's main advantage is to not require (in the blind source separation context) a prewhitening stage, which allows them to work even with a class of correlated signals and provides generally improved separation performance. Finally, an analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones

  • Nonorthogonal Joint Diagonalization/Zero Diagonalization for Source Separation Based on Time-Frequency Distributions
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: E M Fadaili, N T Moreau, Eric Moreau
    Abstract:

    This paper deals with the blind separation of instantaneous mixtures of source signals using time-frequency distributions (Tfds). We propose iterative algorithms to perform the nonorthogonal zero diagonalization and/or joint diagonalization of given sets of matrices. As an application, we show that the source separation can be realized by applying one of these algorithms to a set of spatial Quadratic Tfd matrices corresponding only to the so-called cross-source terms and/or to the so-called autosource terms. The determination of the above matrices to be jointly decomposed requires first an automatic selection procedure of useful time-frequency points. Regarding this last point, we also propose a new selection procedure and a modification of an existing one and provide a comparison with other existing ones. The nonorthogonal joint diagonalization and/or zero diagonalization algorithm's main advantage is to not require (in the blind source separation context) a prewhitening stage, which allows them to work even with a class of correlated signals and provides generally improved separation performance. Finally, an analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones

E M Fadaili - One of the best experts on this subject based on the ideXlab platform.

  • nonorthogonal joint diagonalization zero diagonalization for source separation based on time frequency distributions
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: E M Fadaili, N T Moreau, Eric Moreau
    Abstract:

    This paper deals with the blind separation of instantaneous mixtures of source signals using time-frequency distributions (Tfds). We propose iterative algorithms to perform the nonorthogonal zero diagonalization and/or joint diagonalization of given sets of matrices. As an application, we show that the source separation can be realized by applying one of these algorithms to a set of spatial Quadratic Tfd matrices corresponding only to the so-called cross-source terms and/or to the so-called autosource terms. The determination of the above matrices to be jointly decomposed requires first an automatic selection procedure of useful time-frequency points. Regarding this last point, we also propose a new selection procedure and a modification of an existing one and provide a comparison with other existing ones. The nonorthogonal joint diagonalization and/or zero diagonalization algorithm's main advantage is to not require (in the blind source separation context) a prewhitening stage, which allows them to work even with a class of correlated signals and provides generally improved separation performance. Finally, an analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones

  • Nonorthogonal Joint Diagonalization/Zero Diagonalization for Source Separation Based on Time-Frequency Distributions
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: E M Fadaili, N T Moreau, Eric Moreau
    Abstract:

    This paper deals with the blind separation of instantaneous mixtures of source signals using time-frequency distributions (Tfds). We propose iterative algorithms to perform the nonorthogonal zero diagonalization and/or joint diagonalization of given sets of matrices. As an application, we show that the source separation can be realized by applying one of these algorithms to a set of spatial Quadratic Tfd matrices corresponding only to the so-called cross-source terms and/or to the so-called autosource terms. The determination of the above matrices to be jointly decomposed requires first an automatic selection procedure of useful time-frequency points. Regarding this last point, we also propose a new selection procedure and a modification of an existing one and provide a comparison with other existing ones. The nonorthogonal joint diagonalization and/or zero diagonalization algorithm's main advantage is to not require (in the blind source separation context) a prewhitening stage, which allows them to work even with a class of correlated signals and provides generally improved separation performance. Finally, an analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones