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B Boashash - One of the best experts on this subject based on the ideXlab platform.
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Parameter Selection for Optimising Time-Frequency Distributions and Measurements of Time-Frequency Characteristics of Non-Stationary Signals
2020Co-Authors: B Boashash, Victor SucicAbstract:The Quadratic class of time-frequency distributions (Tfds) forms a set of tools which allow to effectively extract important information from a nonstationary signal. To determine which TFD best represents the given signal, it is a common practice to visually compare different Tfds' time-frequency plots, and select as best the TFD with the most appealing plot. This visual comparison is not only subjective, but also difficult and unreliable especially when signal components are closely-spaced in the time-frequency plane. To objectively compare Tfds, a quantitative performance measure should be used. Several measures of concentration/complexity have been proposed in the literature. However, those measures by being derived with certain theoretical assumptions about Tfds are generally not suitable for the TFD selection problem encountered in practical applications. The non-existence of practically-valuable measures for Tfds' resolution comparison, and hence the non-existence of methodologies for the signal optimal TFD selection, has significantly limited the use of time-frequency tools in practice. In this thesis, by extending and complementing the concept of spectral resolution to the case of nonstationary signals, and by redefining the set of Tfds' properties desirable for practical applications, we define an objective measure to quantify the quality of Tfds. This local measure of Tfds' resolution performance combines all important signal time-varying parameters, along with Tfds' characteristics that influence their resolution. Methodologies for automatically selecting a TFD which best suits a given signal, including real-life signals, are also developed. The optimisation of the resolution performances of Tfds, by modifying their kernel filter parameters to enhance the Tfds' resolution capabilities, is an important prerequisite in satisfying any additional application-specific requirements by the Tfds. The resolution performance measure and the accompanying Tfds' comparison criteria allow to improve procedures for designing high-resolution Quadratic Tfds for practical time-frequency analysis. The separable kernel Tfds, designed in this way, are shown to best resolve closely-spaced components for various classes of synthetic and real-life signals that we have analysed.
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ISSPA - A computationally efficient implementation of Quadratic time-frequency distributions
2007 9th International Symposium on Signal Processing and Its Applications, 2020Co-Authors: John M. O'toole, Mostefa Mesbah, B BoashashAbstract:Time-frequency distributions (Tfds) are computationally intensive methods. A very common class of Tfds, namely Quadratic Tfds, is obtained by time-frequency (TF) smoothing the Wigner Ville distribution (WVD). In this paper a computationally efficient implementation of this class of Tfds is presented. In order to avoid artifacts caused by circular convolution, linear convolution is applied in both the time and frequency directions. Four different kernel types are identified and separate optimised implementations are presented for each kernel type. The computational complexity is presented for the different kernel types.
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Time Frequency Analysis - Chapter 3 - Theory of Quadratic Tfds
Time Frequency Analysis, 2020Co-Authors: B BoashashAbstract: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.
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Optimisation of the realisation of Quadratic discrete time-freqeuncy distributions as a Matlab toolbox
2020Co-Authors: John M. O'toole, B BoashashAbstract: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.
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Time Frequency Analysis - Chapter 6 - Implementation and Realization of Tfds
Time Frequency Analysis, 2020Co-Authors: B BoashashAbstract:This chapter discusses the implementation and realization of time frequency distribution (TFD). It presents procedures, techniques, and methodologies for the efficient implementation of Tfds. The discrete-time equivalent formulation of Quadratic Tfds is defined for the purpose of digital computation. An alternative method for realization of Quadratic Tfds is to use the short-time Fourier transform (STFT) as a basis. The Gabor time–frequency representation may be expanded on a rectangular lattice, using the Fourier and Zak transforms for direct implementations. The computation of other Quadratic Tfds can also be facilitated by using spectrogram decomposition. The chapter outlines the computational procedure for implementing Quadratic time–frequency methods directly, along with the necessary algorithms and MATLAB TM code fragments. Use of a common algorithm for all Tfds is convenient for the programmer; efficiency can sometimes be improved by using different algorithms in special cases.
B Boashash - One of the best experts on this subject based on the ideXlab platform.
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a comparison of Quadratic Tfds for entropy based detection of components time supports in multicomponent nonstationary signal mixtures
International Workshop on Systems Signal Processing and their Applications, 2013Co-Authors: Nicoletta Saulig, Victor Sucic, B Boashash, Damir SersicAbstract:Separation of different signal components, produced by one or more sources, is a problem encountered in many signal processing applications. This paper proposes a fully automatic undetermined blind source separation method, based on a peak detection and extraction technique from a signal time-frequency distribution (TFD). Information on the local number of components is obtained from the TFD Short-term Renyi entropy. It also allows to detect components time supports in the time-frequency plane, with no need for predefined thresholds on the components amplitude. This approach allows to extract different signal components without prior knowledge about the signal. The method is also used as a quality criterion to compare Quadratic Tfds. Results for synthetic and real data are reported for different Tfds, including the recently introduced Extended Modified B distribution.
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resolution performance assessment for Quadratic Tfds
TIme-Frequency Signal Analysis and Processing: A Comprehensive Reference, 2003Co-Authors: B Boashash, Victor SucicAbstract:Quadratic time-frequency distributions (Tfds) are effective tools for extracting information from a non-stationary signal, such as the number of components, their durations and bandwidths, components’ relative amplitudes and instantaneous frequency (IF) laws (see Chapters 1 and 2). The performance of Tfds depends on the type of signal (see Chapter 3) [1,2]. For example, in the case of a monocomponent linear FM signal, the Wigner-Ville distribution is known to be optimal in the sense that it achieves the best energy concentration around the signal IF law (see Article 2.1 for more details) [1]. In applications involving multicomponent signals, choosing the right TFD to analyze the signals is an immediate critical task for the signal analyst. How best to make this assessment, using current knowledge, is the subject of this article. Let us, for example, consider a multicomponent whale signal, represented in the time-frequency domain using the Wigner-Ville distribution, the spectrogram, the Choi-Williams distribution, the Born-Jordan distribution, the Zhao-Atlas-Marks (ZAM) distribution, and the recently introduced B-distribution [3] (see Fig. 7.4.1). To determine which of the Tfds in Fig. 7.4.1 “best” represents this whale signal (i.e. which one gives the best components’ energy concentration and best interference terms suppression, and allows the best estimation of the components’ IF laws) one could visually compare the six plots and choose the most appealing. The spectrogram and the B-distribution, being almost free from the cross-terms, seem to perform best. The performance comparison based on the visual inspection of the plots becomes more difficult and unreliable, however, when the signal components are closelyspaced in the time-frequency plane. To objectively compare the plots in Fig. 7.4.1 requires to use a quantitative performance measure for Tfds. There have been several attempts to define objective measures of “complexity” for Tfds (see Section 7.3.1). One of these measures, the Renyi entropy given in [4], has been used by several authors in preference to e.g. the bandwidth–duration product given in [1]. The performance measure described in this article, unlike the Renyi entropy, is a local measure of the TFD resolution performance, and is thus more suited to the selection problem illustrated by Fig. 7.4.1. This measure takes into account the characteristics of Tfds that influence their resolution, such as energy concentration, components separation, and interference terms minimization. Methodologies for choosing a TFD which best suits a given signal can then be developed by optimizing the resolution performance of considered Tfds and modifying their parameters to better match application-specific requirements.
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Resolution measure criteria for the objective assessment of the performance of Quadratic time-frequency distributions
IEEE Transactions on Signal Processing, 2003Co-Authors: B Boashash, V. SucicAbstract:This paper presents the essential elements for developing objective methods of assessment of the performance of time-frequency signal analysis techniques. We define a measure for assessing the resolution performance of time-frequency distributions (Tfds) in separating closely spaced components in the time-frequency domain. The measure takes into account key attributes of Tfds, such as components mainlobes and sidelobes and cross-terms. The introduction of this measure allows to quantify the quality of Tfds instead of relying solely on visual inspection of their plots. The method of assessment of performance of Tfds also allows the improvement of methodologies for designing high-resolution Quadratic Tfds for time-frequency analysis of multicomponent signals. Different Tfds, including the modified B distribution, are optimized using this methodology. Examples of a performance comparison of Quadratic Tfds in resolving closely spaced components in the time-frequency domain, using the proposed resolution measure, are provided.
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A resolution performance measure for Quadratic time-frequency distributions
Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496), 2000Co-Authors: B Boashash, V. SucicAbstract:This paper presents two novel results which are significant for the application of time-frequency signal analysis techniques to real life signals. First, we introduce a measure for comparing the resolution performance of Tfds in separating closely spaced components in the time-frequency domain. The measure takes into account key attributes of Tfds such as main-lobes, side-lobes, and cross-terms. The introduction of this measure is an improvement of current techniques which rely on visual inspection of plots. The second result consists in proposing a methodology for designing high resolution Quadratic Tfds for the time-frequency analysis of multicomponent signals when components are close to each other. A recently introduced TFD, the B-distribution, and its modified version are defined using this methodology. Finally, the performance comparison of Quadratic Tfds using the proposed resolution measure shows that the B-distribution outperforms existing Quadratic Tfds in resolving closely spaced components in the time-frequency domain.
Adel Belouchrani - One of the best experts on this subject based on the ideXlab platform.
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Source Separation and Localization Using Time-Frequency Distributions: An Overview
IEEE Signal Processing Magazine, 2013Co-Authors: Adel Belouchrani, Moeness G. Amin, Nadege Thirion-moreau, Yimin D. ZhangAbstract:In this article, we describe the role of time-frequency distributions (Tfds) in array processing. We particularly focus on Quadratic Tfds (QTfds). We demonstrate how these distributions can be properly integrated with the spatial dimension to enhance individual source signal recovery and angular estimation. The framework that enables such integration is referred to as spatial TFD (STFD). We present the important milestones of STfds that have been reached during the last 15 years. Most importantly, we show that array processing creates new perspectives of QTfds and defines new roles to the autoterms and cross-terms in both problem formulation and solution. Multisensor configurations, in essence, establish a different paradigm and introduces new challenges that did not exist in a single-sensor time-frequency distribution.
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Time-Frequency Distributions Based on Compact Support Kernels: Properties and Performance Evaluation
IEEE Transactions on Signal Processing, 2012Co-Authors: Mansour Abed, Adel Belouchrani, Mohamed Cheriet, B BoashashAbstract: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 multicomponent 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.
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Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain
IEEE Transactions on Signal Processing, 2007Co-Authors: Abdeldjalil Aissa-el-bey, Adel Belouchrani, Nguyen Linh-trung, Karim Abed-meraim, Yves GrenierAbstract:This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses Quadratic time-frequency distributions (Tfds) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses Quadratic Tfds and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones
Victor Sucic - One of the best experts on this subject based on the ideXlab platform.
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Parameter Selection for Optimising Time-Frequency Distributions and Measurements of Time-Frequency Characteristics of Non-Stationary Signals
2020Co-Authors: B Boashash, Victor SucicAbstract:The Quadratic class of time-frequency distributions (Tfds) forms a set of tools which allow to effectively extract important information from a nonstationary signal. To determine which TFD best represents the given signal, it is a common practice to visually compare different Tfds' time-frequency plots, and select as best the TFD with the most appealing plot. This visual comparison is not only subjective, but also difficult and unreliable especially when signal components are closely-spaced in the time-frequency plane. To objectively compare Tfds, a quantitative performance measure should be used. Several measures of concentration/complexity have been proposed in the literature. However, those measures by being derived with certain theoretical assumptions about Tfds are generally not suitable for the TFD selection problem encountered in practical applications. The non-existence of practically-valuable measures for Tfds' resolution comparison, and hence the non-existence of methodologies for the signal optimal TFD selection, has significantly limited the use of time-frequency tools in practice. In this thesis, by extending and complementing the concept of spectral resolution to the case of nonstationary signals, and by redefining the set of Tfds' properties desirable for practical applications, we define an objective measure to quantify the quality of Tfds. This local measure of Tfds' resolution performance combines all important signal time-varying parameters, along with Tfds' characteristics that influence their resolution. Methodologies for automatically selecting a TFD which best suits a given signal, including real-life signals, are also developed. The optimisation of the resolution performances of Tfds, by modifying their kernel filter parameters to enhance the Tfds' resolution capabilities, is an important prerequisite in satisfying any additional application-specific requirements by the Tfds. The resolution performance measure and the accompanying Tfds' comparison criteria allow to improve procedures for designing high-resolution Quadratic Tfds for practical time-frequency analysis. The separable kernel Tfds, designed in this way, are shown to best resolve closely-spaced components for various classes of synthetic and real-life signals that we have analysed.
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A comparison of Quadratic Tfds for entropy based detection of components time supports in multicomponent nonstationary signal mixtures
2013 8th International Workshop on Systems Signal Processing and their Applications (WoSSPA), 2013Co-Authors: Nicoletta Saulig, B Boashash, Victor Sucic, Damir SeršićAbstract:Separation of different signal components, produced by one or more sources, is a problem encountered in many signal processing applications. This paper proposes a fully automatic undetermined blind source separation method, based on a peak detection and extraction technique from a signal time-frequency distribution (TFD). Information on the local number of components is obtained from the TFD Short-term Rényi entropy. It also allows to detect components time supports in the time-frequency plane, with no need for predefined thresholds on the components amplitude. This approach allows to extract different signal components without prior knowledge about the signal. The method is also used as a quality criterion to compare Quadratic Tfds. Results for synthetic and real data are reported for different Tfds, including the recently introduced Extended Modified B distribution.
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a comparison of Quadratic Tfds for entropy based detection of components time supports in multicomponent nonstationary signal mixtures
International Workshop on Systems Signal Processing and their Applications, 2013Co-Authors: Nicoletta Saulig, Victor Sucic, B Boashash, Damir SersicAbstract:Separation of different signal components, produced by one or more sources, is a problem encountered in many signal processing applications. This paper proposes a fully automatic undetermined blind source separation method, based on a peak detection and extraction technique from a signal time-frequency distribution (TFD). Information on the local number of components is obtained from the TFD Short-term Renyi entropy. It also allows to detect components time supports in the time-frequency plane, with no need for predefined thresholds on the components amplitude. This approach allows to extract different signal components without prior knowledge about the signal. The method is also used as a quality criterion to compare Quadratic Tfds. Results for synthetic and real data are reported for different Tfds, including the recently introduced Extended Modified B distribution.
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resolution performance assessment for Quadratic Tfds
TIme-Frequency Signal Analysis and Processing: A Comprehensive Reference, 2003Co-Authors: B Boashash, Victor SucicAbstract:Quadratic time-frequency distributions (Tfds) are effective tools for extracting information from a non-stationary signal, such as the number of components, their durations and bandwidths, components’ relative amplitudes and instantaneous frequency (IF) laws (see Chapters 1 and 2). The performance of Tfds depends on the type of signal (see Chapter 3) [1,2]. For example, in the case of a monocomponent linear FM signal, the Wigner-Ville distribution is known to be optimal in the sense that it achieves the best energy concentration around the signal IF law (see Article 2.1 for more details) [1]. In applications involving multicomponent signals, choosing the right TFD to analyze the signals is an immediate critical task for the signal analyst. How best to make this assessment, using current knowledge, is the subject of this article. Let us, for example, consider a multicomponent whale signal, represented in the time-frequency domain using the Wigner-Ville distribution, the spectrogram, the Choi-Williams distribution, the Born-Jordan distribution, the Zhao-Atlas-Marks (ZAM) distribution, and the recently introduced B-distribution [3] (see Fig. 7.4.1). To determine which of the Tfds in Fig. 7.4.1 “best” represents this whale signal (i.e. which one gives the best components’ energy concentration and best interference terms suppression, and allows the best estimation of the components’ IF laws) one could visually compare the six plots and choose the most appealing. The spectrogram and the B-distribution, being almost free from the cross-terms, seem to perform best. The performance comparison based on the visual inspection of the plots becomes more difficult and unreliable, however, when the signal components are closelyspaced in the time-frequency plane. To objectively compare the plots in Fig. 7.4.1 requires to use a quantitative performance measure for Tfds. There have been several attempts to define objective measures of “complexity” for Tfds (see Section 7.3.1). One of these measures, the Renyi entropy given in [4], has been used by several authors in preference to e.g. the bandwidth–duration product given in [1]. The performance measure described in this article, unlike the Renyi entropy, is a local measure of the TFD resolution performance, and is thus more suited to the selection problem illustrated by Fig. 7.4.1. This measure takes into account the characteristics of Tfds that influence their resolution, such as energy concentration, components separation, and interference terms minimization. Methodologies for choosing a TFD which best suits a given signal can then be developed by optimizing the resolution performance of considered Tfds and modifying their parameters to better match application-specific requirements.
Taoufik Ben-jabeur - One of the best experts on this subject based on the ideXlab platform.
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Time-frequency features for pattern recognition using high-resolution Tfds
Digital Signal Processing, 2015Co-Authors: B Boashash, Nabeel Ali Khan, Taoufik Ben-jabeurAbstract:This paper presents a tutorial review of recent advances in the field of time-frequency ( t , f ) signal processing with focus on exploiting ( t , f ) image feature information using pattern recognition techniques for detection and classification applications. This is achieved by (1) revisiting and streamlining the design of high-resolution Quadratic time frequency distributions (Tfds) so as to produce adequate ( t , f ) images, (2) using image enhancement techniques to improve the resolution of Tfds, and (3) defining new ( t , f ) features such as ( t , f ) flatness and ( t , f ) entropy by extending time-domain or frequency-domain features. Comparative results indicate that the new ( t , f ) features give better performance as compared to time-only or frequency-only features for the detection of abnormalities in newborn EEG signals. Defining high-resolution Tfds for the extraction of new ( t , f ) features further improves performance. The findings are corroborated by new experimental results, theoretical derivations and conceptual insights. A streamlined methodology for designing high resolution Quadratic Tfds using separable, directional and adaptive kernels.A formulation of new (t, f) features by translation from time-domain only features or frequency-domain only features.A review of (t, f) image processing techniques for resolution enhancement, de-noising and improved classification.A review of multi-component IF estimation techniques as a performance criterion to compare time-frequency distributions.Experiments that illustrate the above points in EEG seizure detection and classification using a large medical database.
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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), 2012Co-Authors: B Boashash, Taoufik Ben-jabeurAbstract: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.
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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), 2012Co-Authors: B Boashash, Taoufik Ben-jabeurAbstract: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.
