This paper presents a time-frequency approach for fetal movement monitoring which is based on the instantaneous amplitude (IA) and instantaneous frequency (IF) of signals collected using 3axial accelerometers placed over the maternal abdomen. Results of a feature selection method based on receiver operating characteristic analysis shows that the mean of the IAs and deviation of the Ifs outperform other features. A support vector machine based classifier which uses these 2 features exhibits a total accuracy of 96.6% with reasonably high sensitivity and specificity.

This study proposes an adaptive method for components instantaneous frequency (IF) estimation of noisy non‐stationary multicomponent signals, combined with the components time‐support estimation method based on the short‐time Rényi entropy (STRE). Components localisation and separation are done using a double‐direction component tracking and extraction method presented here, while the IF estimation is done using the adaptive algorithms based on the intersection of confidence intervals (ICI) rule and the relative intersection of confidence intervals (RICI) rule. The results obtained using the ICI and RICI rules are compared for various window types, signal‐to‐noise ratios and time–frequency distributions, both with and without using the information on components time support. Most of the errors in IF estimation using the ICI and RICI‐based methods are caused by imprecise components time‐support estimation. The proposed methods combined with the STRE have achieved a significant accuracy improvement in terms of the mean absolute error and the mean squared error, reducing them by up to 73 and 93%, respectively. The method has been applied to real‐life signals and proven to be an efficient tool for IF estimation of noisy non‐stationary multicomponent signals.

This paper presents a time-frequency approach to detect perinatal hypoxia by characterizing the nonstationary nature of heart rate variability (HRV) signals. Quadratic time-frequency distributions (TFDs) are used to represent the HRV signals. Six features based on the instantaneous frequency (IF) of the lower frequency components of HRV signals are selected to establish a classifier using support vector machine. The classifier is trained and tested using the signals recorded from a neonatal piglet model under a controlled hypoxic condition, which provides reliable annotations on the data. The method shows superior performance in the detection of hypoxic epochs with sensitivity (89.8%), specificity (100%) and total accuracy (94.9%) compared with that based on frequency domain features, indicating that nonstationarity should be taken into account for a more accurate assessment of the newborn status with possible hypoxia when analyzing HRV signals.

This letter presents a novel algorithm to compute the instantaneous frequency (IF) of a multicomponent nonstationary signal using a combination of fractional spectrograms (FS). A high resolution time frequency distribution (TFD) is defined by combining FS computed using windows of varying lengths and chirp rates. The IF of individual signal components is then computed by applying a peak detection and component extraction procedure. The mean square error (MSE) of IF estimates computed with the AFS is lower than the MSE of IF estimates obtained from other TFDs for SNR varying from -5 dB to 16 dB.

This paper introduces the notion of the instantaneous frequency (IF) based generalized phase synchrony in time-frequency analysis based on the concept of cointegration. This phase synchrony is then quantified by investigating the linear relationships between IF laws of nonstationary multivariate signals. The proposed approach is applied to a multichannel newborn EEG signal and the results are compared with that of a bivariate phase synchrony measure.

In this paper, we introduce a radon wigner ville based image dissimilarity measure. The proposed Image distortion measure aims to combine the useful properties of the wigner ville and the directionality of the finite Radon transform for image quality assessment. The results are compared with several HVS and transform based measures of image quality on the basis of complexity of these measures and their consistency with subjective assessment.

This paper presents two new time-frequency distributions based on kernels with compact support (KCS) namely the separable CB (SCB) and the polynomial CB (PCB) TFDs. The implementation of these distributions follows the method developed for the Cheriet-Belouchrani CB TFD. The performance of this family of TFDs is compared to the most known quadratic distributions through tests on multi-component signals with linear and nonlinear frequency modulations (FMs) considering the noise effects as well. Comparisons are based on the evaluation of an objective criterion namely the Boashash-Sucic's normalized instantaneous resolution performance measure that allows to provide the optimized TFD using a specific methodology. In all presented examples, the KCS TFDs have been shown to have a significant interference mitigation, with the component energy concentration around their respective instantaneous frequency laws being well preserved giving high resolution measure values.

In this paper, we propose features extracted from the heart rate variability (HRV) based on the first and second conditional moments of time-frequency distribution (TFD) as an additional guide for seizure detection in newborn. The features of HRV in the low frequency band (LF: 0-0.07 Hz), mid frequency band (MF: 0.07-0.15 Hz), and high frequency band (HF: 0.15-0.6 Hz) have been obtained by means of the time-frequency analysis using the modified-B distribution (MBD). Results of ongoing time-frequency research are presented. Based on our preliminary results, the first conditional moment of HRV which is also known as the mean/central frequency in the LF band and the second conditional moment of HRV which is also known as the variance/instantaneous bandwidth (IB) in the HF band can be used as a good feature to discriminate the newborn seizure from the non-seizure

The paper presents a new method for detecting EEG spikes. The method is based on the time-frequency distribution of the signal. As spikes are short time broadband events, they are represented as ridges in the time-frequency domain. In this domain, the high instantaneous energy of spikes allows them to be distinguishable from the background. To detect spikes, the time-frequency distribution of the signal of interest is first enhanced to attenuate the noise. Two frequency slices of the enhanced time-frequency distribution are then extracted and subjected to the smoothed nonlinear energy operator (SNEO). Finally, the output of the SNEO is thresholded to localise the position of the spikes in the signal. The SNEO is employed to accentuate the spike signature in the extracted frequency slices. A spike is considered to exist in the time domain signal if a signature of the spike is detected at the same position in both frequency slices.

A time-frequency approach for detecting seizure activities in newborns' electroencephalogram (EEG) data is proposed. The discrimination between seizure and non-seizure states is based on the time-frequency distance between the consequent segments in the EEG signal. Three different time-frequency measures and three different reduced time-frequency distributions are used. The proposed method is tested on the EEG data acquired from three neonates with ages ranging from two days to two weeks. The experimental results validate the suitability of the proposed method in automated newborns' seizure detection. The results show an average seizure detection rate of 96% and false alarm rate of 5%.

This paper investigates the performance of four nonparametric newborn EEG seizure detection methods. The authors recently proposed a time-frequency (TF) based technique suitable for nonstationarity of EEG signal. This method attempts to detect seizure activities through analysing the interspike intervals of the EEG in the TF domain. The performance of this method is compared to those of three nonparametric techniques for seizure detection. These methods are: autocorrelation, spectrum and singular spectrum analysis (SSA). The autocorrelation method performs analysis in the time domain and is based on the autocorrelation function of short epochs of EEG data. The spectrum technique is based on spectral analysis and is used to detect periodic discharges. The SSA technique employs singular spectrum analysis and information theoretic-based selection of the signal subspace. These three methods are based on the assumption that newborn EEG signal is quasi-stationary. The obtained results show the superior performance of the TF-based technique for detecting newborn EEG seizures.

A new automated method is proposed to detect seizure events in newborns from electroencephalogram (EEG) data. The detection scheme is based on observing the changing behavior of the wavelet coefficients (WCs) of the EEG signal at different scales. An optimal feature subset is obtained using the mutual information evaluation function (MIEF). The MIEF algorithm evaluates a set of candidate features extracted from WCs to select an informative feature subset. The subset is then fed to an artificial neural network (ANN) classifier that organizes the EEG signal into seizure or non-seizure activity. The performance of the proposed features is compared with that of the features obtained using a mutual information feature selection (MIFS) algorithm. The training and test sets are obtained from EEG data acquired from 5 neonates with ages ranging from 2 days to 2 weeks.

This paper deals with the problem of seizure detection in newborns using the EEG signal. The performance of three techniques for seizure detection is investigated. The technique of Roessgen is model based and uses parameter estimation for detection. The two other methods are non-parametric. The technique of Gotman uses frequency analysis to determine the changes in the dominant peak of the frequency spectrum of short epochs of EEG data. The technique of Liu performs analysis in the time domain and is based on the auto-correlation function of short epochs of EEG data. This paper discusses the underlying methodology of the different techniques and presents a comparison of their performance on simulated EEG signal with the aim of considering the best for a possible implementation within a DSP system for automatic seizure detection. The obtained results show that Gotman's method outperforms the two other methods in terms of good detection, the missing detection, and the false alarm rates.

A novel compression algorithm for fingerprint images is introduced. Using wavelet packets and lattice vector quantization , a new vector quantization scheme based on an accurate model for the distribution of the wavelet coefficients is presented. The model is based on the generalized Gaussian distribution. We also discuss a new method for determining the largest radius of the lattice used and its scaling factor , for both uniform and piecewise-uniform pyramidal lattices. The proposed algorithms aim at achieving the best rate-distortion function by adapting to the characteristics of the subimages. In the proposed optimization algorithm, no assumptions about the lattice parameters are made, and no training and multi-quantizing are required. We also show that the wedge region problem encountered with sharply distributed random sources is resolved in the proposed algorithm. The proposed algorithms adapt to variability in input images and to specified bit rates. Compared to other available image compression algorithms, the proposed algorithms result in higher quality reconstructed images for identical bit rates.

Handover processes in microcellular systems are more involved than in cellular systems. In particular, microcellular systems suffer from the so-called corner effect where line-of-sight between the mobile station and the base station is suddenly lost when the mobile rounds a comer. As a result, the received signal drops rapidly below threshold level and the call can be lost. It has been shown that, if an accurate estimation of the velocity of the mobile unit is available, the call can be rescued by applying short temporal window averaging on the received signal. Current methods for estimating the velocity of mobile units in microcellular systems are based on the level crossing rate of the envelope of the received signals. This paper presents a new velocity estimator based on the instantaneous frequency of the received signal. The performance of the proposed estimator is shown to be superior to that of the level crossing rate method. The average relative error of the proposed estimator is down to below 8% whereas that of the LCR method reaches 14%.

Previous techniques for seizure detection in newborn babies are inefficient. The main reason for their relative poor performance resides in their assumption of stationarity of the EEG. To remedy this problem, we use time-frequency distributions (TFD) to analyse and characterise the newborn EEG seizure patterns as a first step toward a time-frequency (TF) based seizure detection and classification scheme. This paper presents the results of the analysis of these time-frequency patterns for two abnormal newborn EEGs. We demonstrate that the newborn EEG seizures are well described by a class of mono- and multi-component linear FM signals. This result is novel and contradicts the simplistic assumptions routinely made in the field.

The estimation of the scattering function in a time-frequency selective fading mobile environment is considered. The scattering function explicitly reveals the time-frequency selective behavior of the fading channel under the well-known wide-sense stationary Gaussian process with uncorrelated scattering (WSSUS) assumption. We propose two classes of estimators based on a time-frequency framework that generalize the existing estimators while giving an extra freedom according to different criteria wanted to be achieved in the estimation of the scattering function. Instead of using the Woodward ambiguity function or symmetric ambiguity function, we use the generalized ambiguity function which comes from the general class of quadratic time-frequency distributions.

Selecting a time-frequency distribution (TFD) which represents a signal in an optimal way is commonly done by visually comparing plots of different TFD. This paper presents a procedure that allows the analyst to perform the same task in an automatic way. Using the resolution performance measure for TFD, the procedure optimises all distributions considered and selects the one which results into best concentration of signal components around their instantaneous frequency laws, as well as best suppression of the interference terms in the time-frequency plane. To do this requires us to define a methodology to measure the time-frequency characteristics of a signal from its optimal TFD. An algorithm which implements this methodology is described and results are presented.

This paper presents a time-frequency approach for the estimation of the instantaneous frequency (IF) of a linear frequency modulated (FM) signal affected by multiplicative and additive white Gaussian noise. Contrary to earlier claims, we show that the Wigner-Ville spectrum (WVS) is optimal in the sense of IF localisation for such signals and its peak is proposed as an IF estimator. We derive an analytical expression for the asymptotic variance for this estimator. Simulation results based on Monte-Carlo realisations illustrate and confirm the validity of the theoretical derivations and analysis.

Estimation of the instantaneous frequency (IF) of multicomponent FM signals with additive Gaussian noise is considered. A reduced interference distribution (RID) with high resolution is used for time-frequency representation of signals. If the IF law is a nonlinear function of time, the bias and variance of the estimate depend on the window length. The optimal window length for bias-variance tradeoff depends on the unknown IF law, hence calling for an adaptive algorithm with time-varying and data-driven window length to resolve this tradeoff. The adaptive estimation of multiple IF laws is based on tracking the component maxima in the time-frequency plane. Simulation results for multi-component signals are comparable with those obtained for mono-component signals when the components are well separated.

The peak of the polynomial Wigner-Ville distribution is known to be a consistent estimator of the instantaneous frequency for polynomial FM signals. We present an algorithm for the design of an optimal time-varying window length for this estimator when noisy non-linear, not necessarily polynomial, FM signals are considered. The results obtained show that the estimator is accurate and outperforms any fixed window time-frequency distribution based estimator.

This paper considers a system design for processing a multidimensional biomedical signal formed by EEG, ECG, EOG and motion recorded from a newborn, for the purpose of detection of epileptic seizures in newborns as an extension of the method reported in Boashash et al. (1997) and Roessgen et al. (1998). We describe the proposed design, and discuss how the signals will be analysed and fused to detect the occurrence of seizure. We also discuss the role of modelling in refining the signal processing unit.

The Adichie (1984) rank test and signed rank test are adapted for signal detection. We establish a relationship with the correlation between a function of the signal to be detected and the ranks of the observed data. A comparison between the power of these tests and the constant false alarm rate matched filter (CFAR MF) shows that the rank tests perform better when longer observations are available and for the symmetric alpha stable distributions encountered in applications with impulsive interference.

Temporal decomposition (TD) is an effective technique to compress the spectral information of speech through orthogonalization of the matrix of spectral parameters leading to an efficient rate reduction in speech coding applications. The performance of TD is a function of the parameters used. Although "decomposition suitability" of a parameter set is typically defined on the basis of "phonetic relevance" criterion, it can not be directly used in speech coding. Instead, quality evaluation of reconstructed speech is more appropriate. In this paper, we extend our earlier work in this area and attempt to assess several "popular" spectral parameter sets from the viewpoint of decomposition suitability in very low bit-rate speech coding using parametric, perceptually-based spectral, and energy distance measures.

This paper considers the identification of time-invariant bilinear models using observed input-output data. Bilinear models represent a parsimonious class of nonlinear parameterisations and have been used in a variety of applications. However the performance of the bilinear model can be limited in practice when standard least-squares techniques are used, as this leads to biased parameter estimates. Most existing solutions for this problem are restrictive, suboptimal, or computationally intensive. We propose an alternative approach to this identification task by utilising a robust regression technique, known as bandlimited regression, to obtain bilinear parameter estimates with reduced bias. The approach is numerically stable and computationally inexpensive. Simulations are given to demonstrate the usefulness of the technique for bilinear system identification.

We present a non-stationary signal classification algorithm based on a time-frequency representation and a multiple hypothesis test. The time-frequency representation is used to construct a time-dependent quadratic discriminant function. At selected points in time we evaluate the discriminant function and form a set of statistics which are used to test the multiple hypotheses. The multiple hypotheses are treated simultaneously using the sequentially rejective Bonferroni test to control the probability of incorrect classification of one class. We show results for classifying three classes of humpback whale calls. The results demonstrate that this time-frequency method performs favourably when compared with a frequency domain method which assumes stationarity.

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants.

This paper presents the results of the integration of a proposed part-segmentation-based vision system. The first stage of this system extracts the contour of the object using a hybrid first- and second-order differential edge detector. The object defined by its contour is then decomposed into its constituent parts using the part segmentation algorithm given by Bennamoun (1994). These parts are then isolated and modeled with 2D superquadrics. The parameters of the models are obtained by the minimization of a best-fit cost function. The object is then represented by its structural description which is a set of data structures whose predicates represent the constituent parts of the object and whose arguments represent the spatial relationship between these parts. This representation allows the recognition of objects independently of their positions, orientations, or sizes. It is also insensitive to objects with partially missing parts. In this paper, examples illustrating the acquired images of objects, the extraction of their contours, the isolation of the parts, and their fitting with 2D superquadrics are reported. The reconstruction of objects from their structural description is illustrated and improvements are suggested.

We approximate a class of time-varying nonlinear models, called the time-varying Hammerstein series, using basis sequences in order to reduce the number of coefficients required in system modelling. The problem is motivated by the practical need to parsimoniously characterise time-varying nonlinear systems. A significant advantage of the approach is that only a single input-output record is required to obtain least-squares estimates of the model parameters. The judicious selection of basis sequence is also discussed. The method represents a simple and practical time-varying nonlinear system identification procedure. Examples are presented to demonstrate the usefulness of the technique.

This paper proposes and demonstrates a practical parameter estimation scheme for estimating the height, speed, range and acoustic frequency of an overflying aircraft. This scheme is based on the phase of the acoustic signal emitted by the aircraft as heard by a stationary observer. Bootstrap techniques are employed to determine confidence bounds for the aircraft parameters given only a single acoustic realisation. This estimation scheme, and the novel use of the bootstrap, are demonstrated by computer simulation and with aircraft acoustic data which was collected by the authors under accurately monitored experimental conditions.

This paper considers the problem of automatic classification of newborn electroencephalogram (EEG) data in order to diagnose for seizure. It is shown that good detection performance of seizure EEG is possible using a methodology based on a model for the generation of the EEG. This model is derived from the histology and biophysics of a localised portion of the brain and is thus physically motivated. The model based detection scheme is first presented and used to detect seizure in real newborn EEG data. These results are then compared with an alternative classification approach known as the quadratic detection filter (QDF). It is shown that the model based scheme is far superior to the QDF since it is not adversely affected by the variability (or non-stationarity) of EEG data, which hinders the performance of most traditional EEG classifiers (such as the QDF).

This paper develops a novel concept of higher-order moment and cumulant functions in the compress/stretch domain, and their corresponding higher-order spectra in the scale domain. Then higher-order Q time-scale distributions are introduced and their properties are investigated. The importance of the paper is to link the concept of scale signal representations with well established and important methods of higher-order spectral analysis.

This paper considers the problem of seizure detection in the neonate based on electroencephalogram (EEG) data. It is shown that by using a histologically and biophysically justifiable model for the generation of the EEG, the detection of electrographic seizure is greatly improved. The model is presented along with an estimator for the model parameters. Then a simple seizure detection scheme based on the model parameter estimates is suggested. It is also shown that this scheme is superior in performance to spectral analysis techniques such as the periodogram when used to analyse both simulated and real EEG data.

The paper establishes the relationship between the two methods of higher order time-frequency analysis: the polynomial Wigner-Ville distribution (WVD) and the higher order WVD. Using the projection-slice theorem, it is shown that the polynomial WVD represents a unique projection of the higher-order WVD from the time-multifrequency space to the time-frequency subspace. The implication of this relationship is investigated from the aspect of the analysis of multicomponent signals.

A novel technique for filtering a real signal is presented. The method is based upon encoding the signal as an instantaneous frequency (IF) and using IF analysis techniques to recover a filtered version of it. A general iterative time-frequency peak filtering (TFPF) scheme based on this method is formulated. Simulations are given which show extremely clean recovery of signals in noise levels down to -9 dB. Applications to estimating the polynomial phase coefficients of nonstationary signals and differentiating noisy signals are presented.>

Time-varying higher-order spectra (TV-HOS), have recently been proposed for (poly)spectral analysis of non-stationary signals. Two new results are presented here. First, the cumulant TV-HOS (in particular, cumulant Wigner-Ville trispectrum (WVT)), is shown to preserve the essential properties of cumulant higher-order spectra (e.g. eliminate Gaussian additive noise) and at the same time characterise time-variations of the signal's frequency content. Second, when dealing with composite FM signals, a special kind of "non-oscillating cross-terms" is shown to appear in the moment TV-HOS time-frequency subspace. We show that these cross-terms cannot be eliminated by smoothing the WVT, but rather by an appropriate projection from the full time-multi-frequency space to a time-frequency subspace.>

We extend the spectrum estimation method of Thomson (1982, 1990) to non-stationary signals by formulating a multiple window spectrogram. The traditional spectrogram can be represented as a member of Cohen's class of time-frequency distributions (TFDs) where the smoothing kernel is the Wigner distribution of the signal temporal window. We show the unusual shape of the Cohen's class smoothing kernels corresponding to the Thomson method multiple windows. These are a class of smoothing kernels not hitherto used in time-frequency (t-f) analysis. Examples of the multiple window spectrogram applied to a noisy dual linear FM test signal and to actual underwater acoustic data demonstrate the merit of the method.>

This paper presents the results of the integration of a proposed part-segmentation based vision system. The first stage of this system extracts the contour of the object using a hybrid first and second-order differential edge detector. The object defined by its contour is then decomposed into its constituent parts using the part segmentation algorithm proposed by Bennamoun (see Proc. of the IEEE ICASSP'94, p.41-44, Adelaide, Australia, April 1994). These parts are then isolated and modelled with 2-D superquadrics. The parameters of the models are obtained by the minimization of a best-fit cost function. The object is then represented by its structural description which is a set of data structures whose predicates represent the constituent parts of the object and whose arguments represent the spatial relationship between these parts. This representation allows the recognition of objects independently of their positions, orientations or sizes. It is also insensitive to objects with partially missing parts. In this paper, examples illustrating acquired images of objects, the extraction of their contours, the isolation of the parts, and their fitting with 2-D superquadrics are reported. The reconstruction of objects from their structural description is illustrated and improvements are suggested.>

In mobile radio communications, inter-cell handover algorithms represent a critical issue for future pico and micro cellular systems. Two conflicting criteria must be optimized: the number of unnecessary handovers between two adjacent base-stations and the number of lost calls. A handover algorithm is proposed which utilizes a decision criterion such as signal strength. It allows for optimal trade-off between the number of unnecessary handovers and the number of lost calls. It is based on Bayes criterion which is commonly used in detection and estimation techniques. An optimal threshold /spl eta/ is derived using this criterion, which depends on the decision criterion and is dynamically adjusted by taking into account the observations. The decision of handover is made by comparing the distance d between the mobile station and the current base-station to this threshold /spl eta/.>

The Wigner-Ville distribution (WVD) is a second-order time-frequency representation in the sense that it is able to give ideal energy concentration for quadratic phase FM signals, and its expectation value is a second order time-varying spectrum. The generalized WVD (GWVD) is defined by extension so as to achieve ideal energy concentration for higher order phase laws. In addition, by taking the expected value of the GWVD, time-varying higher-order spectra can be defined. The merit of including time-varying higher-order spectral information when analyzing underwater acoustic signals is demonstrated.>

The concept of instantaneous frequency (IF), its definitions, and the correspondence between the various mathematical models formulated for representation of IF are discussed. The extent to which the IF corresponds to the intuitive expectation of reality is also considered. A historical review of the successive attempts to define the IF is presented. The relationships between the IF and the group-delay, analytic signal, and bandwidth-time (BT) product are explored, as well as the relationship with time-frequency distributions. The notions of monocomponent and multicomponent signals and instantaneous bandwidth are discussed. It is shown that these notions are well described in the context of the theory presented.>

For pt.I see ibid., vol.80, no.4, p.520-38 (1992). The concept of instantaneous frequency (IF) is extended to discrete-time signals. The specific problem explored is that of estimating the IF of frequency-modulated (FM) discrete-time signals embedded in Gaussian noise. Well-established methods for estimating the IF include differentiation of the phase and smoothing thereof, adaptive frequency estimation techniques such as the phase locked loop (PLL), and extraction of the peak from time-varying spectral representations. More recently, methods based on a modeling of the signal phase as a polynomial have been introduced. These methods are reviewed, and their performance compared on both simulated and real data. Guidelines are given as to which estimation method should be used for a given signal class and signal-to-noise ratio (SNR).>

Some algorithms for estimating the instantaneous frequency of a constant-amplitude phase-modulated signal are reviewed and compared in terms of computational and statistical efficiency. Each of the algorithms is briefly described. The computational requirements for each algorithm are presented in tabular form, and the variance of each estimator (obtained through simulation) is plotted against theoretically derived lower variance bounds. An explanation is provided as to why each estimator performs as it does, and recommendations are given for the method which should be used for a given signal class.>

A method to process a vibroseis vertical seismic profile (VSP) borehole signal in the time-frequency plane by using the cross Wigner-Ville distribution (XWVD) is presented. The resultant method is a mathematically robust extension of existing traditional techniques which allows for the attenuation of undesirable components and time-variant spectral compensation; qualities which are all difficult to achieve. The method shows that a time-frequency processing of vibroseis seismic data can be performed while maintaining the mathematical purity of classical techniques.>

An automatic time-varying filter design technique is presented, based on windowing in the time-frequency plane about the IF of the signal under analysis, followed by signal synthesis using the Wigner-Ville distribution. The choice of the IF estimation algorithm determines the performance of the method. Algorithms for IF estimation are presented, and their performance in additive noise is discussed. The method is applicable to automatic filtering of FM signals. A review is presented of the various approaches followed by the authors and others.>

The definitions of instantaneous frequency are reviewed in the context of signal theory, communication theory and discrete time implementations. The spread of a signal about its instantaneous frequency, or instantaneous bandwidth, is investigated for several common time-frequency distributions by simulations. The instantaneous frequency of a multicomponent signal is examined. Further investigation of the time-frequency representation of a multicomponent signal leads to an adaptive algorithm which may improve time-frequency resolution of multicomponent signals.>

A method based on an iterative procedure incorporating time-frequency distributions (TFDs) is proposed for instantaneous frequency (IF) estimation of rapidly time-varying signals. This method is then applied to the problem of adaptively detecting a transient of unknown waveshape in white Gaussian noise. For this type of adaptive detection, the signal's time-frequency representation is first estimated, and this estimate is used as the true representation in a time-frequency correlator detector. The IF is assumed to be a critical feature of the transient. Accordingly, the IF is first estimated, and this estimate is then used as an aid to estimate the time-frequency representation of the true signal. This representation is then correlated with the time-frequency representation of the observed signal to provide the appropriate detection statistics.>

Consideration is given to the generalization of stationary cross spectral analysis methods to a class of nonstationary processes, specifically, the class of semistationary finite energy processes possessing sample functions that are of finite energy almost surely. A new quantity called the time-frequency coherence (TFC) is defined, and it is demonstrated that its properties are analogous to those possessed by the stationary coherence function. The problem of estimating the TFC by using elements of L. Cohen's (1966) class of joint time-frequency representations is investigated. It is shown that the only admissible estimators are those based on the class of time-frequency smoothed periodograms. Thus, the familiar procedure of segmentation and (smoothed) short-time Fourier analysis cannot be improved upon (within the framework considered) by the use of the higher-resolution nonparametric time-frequency methods. Procedures for selection of the appropriate estimators and a possible application are suggested.>

It is argued that the Wigner-Ville time-frequency distribution (WVD) of ECG (electrocardiography) signals reveals additional information that is not apparent in the time domain. The energy distribution and the presence of cross terms in the WVD images are heuristically interpreted on the basis of underlying electrophysiology of the human heart. Using these interpretations, time-frequency domain detection of P waves is examined, and the WVD cross terms are shown to be useful.>

The Wigner-Ville distribution (WVD) and the cross Wigner-Ville distribution (XWVD) are applied to signal detection and classification, and signal-to-noise ratio (SNR) performance is discussed. The method is applied to signaturing the individual cylinders of a diesel engine. A comparison with the short-time Fourier transform is provided.>

The Wigner-Ville distribution (WVD) has been shown to concentrate signal energy along the instantaneous frequency law of an emitted Vibroseis source signal. Thus, the WVD is proposed as a basis for achieving event separation for a received Vibroseis signal in the time-frequency (t-f) plane. The WVD has previously been used to determine Earth absorption parameters from the first down going arrival of a Vibroseis signal from a vertical seismic profile (VSP). This method can be extended to the multicomponent signal case, but only if a successful t-f plane event separation can be achieved. This is obtained by using the cross Wigner-Ville distribution (XWVD). The authors also show that the XWVD can be used as the basis for absorption and dispersion determination from a received Vibroseis signal, and for a two dimensional processing of VSP data.>

Nonstationary signals are partitioned into near-stationary segments using a modified Appel and Brandt algorithm. The modification requires two spectral distance measures to be used to produce an algorithm which is insensitive to changes in signal energy level which are irrelevant in this application. Performance on real and simulated data is presented. Segmentation has been used to provide an estimator of the evolutive spectrum, an application to a noisy communication signal is presented.>

The computation and characteristics of two new representations of single lead electrocardiogram data, both based upon the analytic signal corresponding to the waveform, are presented. The first method, employing a complex plane plot of the analytic signal, emphasizes waveform shape independently of time base; the second, a time-frequency representation using the Wigner-Ville distribution, appears to highlight instantaneous frequency variation within the waveform. Both are potentially useful when the patterns are displayed using contour plots, and a specific computerised pattern recognition technique is suggested and some results presented.

The Wigner-Ville Distribution (WVD) has recently been shown to be a valuable tool for time-Frequency Signal Analysis. Its first order moments yield directly the instantaneous frequency of the Signal. The problem of applying a window to the WVD is shown to be the same as that occurring when one uses the Fourier Transform. The choice of any classical window does not affect the estimation of the instantaneous frequency fi(t) in both deterministic and random cases. It is shown that the WVD estimator of the "evolutive spectrum" is unbiased in both time and frequency. Accuracy and statistical stability of the method are discussed. Its application to the analysis of microstructure temperature gradient signals shows that the WVD exhibits more information about the turbulence effect than the Short Time Fourier Transform.

Among the time-frequency distributions, the Wigner distribution (WD) is found to be one of the most powerful tools for time-frequency analysis. We have therefore developed an interactive simulator for time-frequency analysis based on a discrete version of the WD. The WD behavior is then studied for any frequency modulated and time limited signal. The properties of the WD make possible the detection of time-varying signals in the time-frequency domain. An application is presented where the problem is to automatically detect moving bubbles formed in the human blood under hyperbaric environments. We show that time-frequency analysis by means of the WD is an appropriate method to discriminate the bubble signals from the noise. We present some of our results.

Among the various methods of analysing time-varying signals, one of the most interesting is WIGNER-VILLE's. - In the case of signals with a large bandwidth-duration BT product, we recall that their behaviour in the time-frequency domain can be reduced to just two typical cases. The numerical studies performed on different examples are in good agreement with the analytical ones and lead to the possibility of modeling signals in the time-frequency domain. -In the case of signals with a BT product of any magnitude, we study in detail, analytically, and numerically the WIGNER-VILLE representation of linearly frequency modulated signals. These results are then compared with those obtained by usual methods such as the "Moving Window Method" (MWM). The performance of each method is evaluated and ways of optimizing MWM are proposed.