Principle and application of time-frequency analysis by means of the Wigner-Ville transform

The Wigner-Ville transform is known to be a very powerful tool for signal processing in the time frequency plane . This paper is devoted to emphasize the capability and versatility of this transform with special focus on interpretation problems and practical realization requirements . The problem of efficiently smoothing a Wigner- Ville distribution is addressed and solutions are proposed to improve the performances obtained via short-time Fourier analyses . This defines a very general non parametric framework, including the time frequency analysis of deterministic signals as well as estimation procedures for time-varying spectra of non-stationary processes .La transformation de Wigner-Ville occupe une place centrale dans l'analyse temps-fréquence des signaux . On se propose dans cet article de rappeler l'intérêt d'une telle transformation en insistant sur les problèmes pratiques posés par sa mise en aeuvre et son interprétation . On discute particulièrement le choix des fonctions de lissage à utiliser pour obtenir des performances supérieures à celles des méthodes classiques à base de transformée de Fourier à court terme. Ceci fournit un cadre non paramétrique très général, tant pour l'analyse de signaux déterministes modulés que pour l'estimation de spectres dépendant du temps dans le cas de processus non stationnaires

Identification and Restoration of a Class of Aliased Signals

A fundamental theorem of Digital Signal Processing is Shannon's sampling theorem, whichdictates the minimum rate (called the Nyquist rate") at which a continuous-time signalmust be sampled in order to faithfully reproduce the signal from its samples. If a signalcan be reproduced from its samples, then clearly no information about the original signalhas been lost in the sampling process. However, when a signal is sampled at a rate lowerthan the Nyquist Rate, the true spectral content of the original signal is distorted due toaliasing," wherein frequencies in the original signal greater than the sampling frequencyappear as lower frequencies in the sampled signal. This distortion is generally held to beirrecoverable, i.e., whenever aliasing occurs, information is considered to be inevitably lost.This research challenges this notion and presents a technique for identifying aliasingand recovering an unaliased version of a signal from its aliased samples. The method isapplicable to frequency-modulated (FM) signals with a continuous instantaneous frequency(IF), and utilizes analysis of the IF of the aliased signal to 1) determine whether the signalhas potentially been aliased and, if so, 2) compensate for the aliasing by reconstructingan estimate of the true IF of the signal. Time-frequency methods are used to analyzethe potentially aliased signal and estimate the IF, together with modulation, re-samplingand interpolation stages to reconstruct an estimate of the unaliased signal. The proposedtechnique can yield excellent reconstruction of FM signals given ideal estimates of the IF

Real-time spectral modelling of audio for creative sound transformation

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

A Statistical Perspective of the Empirical Mode Decomposition

This research focuses on non-stationary basis decompositions methods in time-frequency analysis. Classical methodologies in this field such as Fourier Analysis and Wavelet Transforms rely on strong assumptions of the underlying moment generating process, which, may not be valid in real data scenarios or modern applications of machine learning. The literature on non-stationary methods is still in its infancy, and the research contained in this thesis aims to address challenges arising in this area. Among several alternatives, this work is based on the method known as the Empirical Mode Decomposition (EMD). The EMD is a non-parametric time-series decomposition technique that produces a set of time-series functions denoted as Intrinsic Mode Functions (IMFs), which carry specific statistical properties. The main focus is providing a general and flexible family of basis extraction methods with minimal requirements compared to those within the Fourier or Wavelet techniques. This is highly important for two main reasons: first, more universal applications can be taken into account; secondly, the EMD has very little a priori knowledge of the process required to apply it, and as such, it can have greater generalisation properties in statistical applications across a wide array of applications and data types. The contributions of this work deal with several aspects of the decomposition. The first set regards the construction of an IMF from several perspectives: (1) achieving a semi-parametric representation of each basis; (2) extracting such semi-parametric functional forms in a computationally efficient and statistically robust framework. The EMD belongs to the class of path-based decompositions and, therefore, they are often not treated as a stochastic representation. (3) A major contribution involves the embedding of the deterministic pathwise decomposition framework into a formal stochastic process setting. One of the assumptions proper of the EMD construction is the requirement for a continuous function to apply the decomposition. In general, this may not be the case within many applications. (4) Various multi-kernel Gaussian Process formulations of the EMD will be proposed through the introduced stochastic embedding. Particularly, two different models will be proposed: one modelling the temporal mode of oscillations of the EMD and the other one capturing instantaneous frequencies location in specific frequency regions or bandwidths. (5) The construction of the second stochastic embedding will be achieved with an optimisation method called the cross-entropy method. Two formulations will be provided and explored in this regard. Application on speech time-series are explored to study such methodological extensions given that they are non-stationary

The automatic classification of the modulation type of communication signals

Available from British Library Document Supply Centre-DSC:DXN013206 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Phase extraction of non-stationary signals produced in dynamic interferometry involving speckle waves

It is now widely acknowledged, among communities of researchers and engineers of very different horizons, that speckle interferometry (SI) offers powerful techniques to characterize mechanical rough surfaces with a submicronic accuracy in static or quasi-static regime, when small displacements are involved (typically several microns or tens of microns). The issue of dynamic regimes with possibly large deformations (typically several hundreds of microns) is still topical and prevents an even more widespread use of speckle techniques. This is essentially due to the lack of efficient processing schemes able to cope with non-stationary AM-FM interferometric signals. In addition, decorrelation-induced phase errors represent an hindrance to accurate measurement when such large displacements and classical fringe analysis techniques are considered. This work is an attempt to address those issues and to endeavor to make the most of speckle interferometry signals. Our answers to those problems are located on two different levels. First of all, we adopt the temporal analysis approach, i.e. the analysis of the temporal signal of each pixel of the sensor area used to record the interferograms. A return to basics of phase extraction is operated to properly identify the conditions under which the computed phase is meaningful and thus give some insight on the physical phenomenon under analysis. Due to their intrinsic non-stationary nature, a preprocessing tool is missing to put the SI temporal signals in a shape which ensures an accurate phase computation, whichever technique is chosen. This is where the Empirical Mode Decomposition (EMD) intervenes. This technique, somehow equivalent to an adaptive filtering technique, has been studied and tailored to fit with our expectations. The EMD has shown a great ability to remove efficiently the random fluctuating background intensity and to evaluate the modulation intensity. The Hilbert tranform (HT) is the natural quadrature operator. Its use to build an analytical signal from the so-detrended SI signal, for subsequent phase computation, has been studied and assessed. Other phase extraction techniques have been considered as well for comparison purposes. Finally, our answer to the decorrelation-induced phase error relies on the well-known result that the higher the pixel modulation intensity, the lower the random phase error. We took benefit from this result – not only linked to basic SNR considerations, but more specifically to the intrinsic phase structure of speckle fields – with a novel approach. The regions within the pixel signal history classified as unreliable because under-modulated, are purely and simply discarded. An interpolation step with the Delaunay triangulation is carried out with the so-obtained non-uniformly sampled phase maps to recover a smooth phase which relies on the most reliable available data. Our schemes have been tested and discussed with simulated and experimental SI signals. We eventually have developed a versatile, accurate and efficient phase extraction procedure, perfectly able to tackle the challenge of dynamic behaviors characterization, even for displacements and/or deformations beyond the classical limit of the correlation dimensions

Approach for Improved Signal-Based Fault Diagnosis of Hot Rolling Mills

Der hier vorgestellte Ansatz ist in der Lage, zwei spezifische schwere Fehler zu erkennen, sie zu identifizieren, zwischen vier verschiedenen Systemzuständen zu unterscheiden und eine Prognose bezüglich des Systemverhaltens zu geben. Die vorliegende Arbeit untersucht die Zustandsüberwachung des komplexen Herstellungsprozesses eines Warmbandwalzwerks. Eine signalbasierte Fehlerdiagnose und ein Fehlerprognoseansatz für den Bandlauf werden entwickelt. Eine Literaturübersicht gibt einen Überblick über die bisherige Forschung zu verwandten Themen. Es wird gezeigt, dass die große Anzahl vorheriger Arbeiten diese Thematik nicht gelöst hat und dass weitere Untersuchungen erforderlich sind, um eine zufriedenstellende Lösung der behandelten Probleme zu erhalten. Die Entwicklung einer neuen Signalverarbeitungskette und die Signalverarbeitungsschritte sind detailliert dargestellt. Die Klassifikationsaufgabe wird in Fehlerdiagnose, Fehleridentifikation und Fehlerprognose differenziert. Der vorgeschlagene Ansatz kombiniert fünf verschiedene Methoden zur Merkmalsextraktion, nämlich Short-Time Fourier Transformation, kontinuierliche Wavelet Transformation, diskrete Wavelet Transformation, Wigner-Ville Distribution und Empirical Mode Decomposition, mit zwei verschiedenen Klassifikationsalgorithmen, nämlich Support-Vektor Maschine und eine Variation der Kreuzkorrelation, wobei letztere in dieser Arbeit entwickelt wurde. Kombinationen dieser Merkmalsextraktion und Klassifikationsverfahren werden an Walzkraft-Daten aus einer Warmbreitbandstraße angewendet.The approach introduced here is able to detect two specific severe faults, to identify them, to distinguish between four different system states, and to give a prognosis on the system behavior. The presented work investigates the condition monitoring of the complex production process of a hot strip rolling mill. A signal-based fault diagnosis and fault prognosis approach for strip travel is developed. A literature review gives an overview about previous research on related topics. It is shown that the great amount of previous work does not cope with the problems treated in this work and that further investigation is necessary to provide a satisfactory solution. The design of a new signal processing chain is presented and the signal processing steps are detailed. The classification task is differentiated into fault detection, fault identification and fault prognosis. The proposed approach combines five different methods for feature extraction, namely short time Fourier transform, continuous wavelet transform, discrete wavelet transform, Wigner-Ville distribution, and empirical mode decomposition, with two different classification algorithms, namely support vector machine and a variation of cross-correlation, the latter developed in this work. Combinations of these feature extraction and classification methods are applied to rolling force data originating from a hot strip mill