Showing papers on "Continuous wavelet transform published in 2000"

Time-frequency analysis of myoelectric signals during dynamic contractions: a comparative study

Abstract: Introduces nonstationary signal analysis methods to analyze the myoelectric (ME) signals during dynamic contractions by estimating the time-dependent spectral moments. The time-frequency analysis methods including the short-time Fourier transform, the Wigner-Ville distribution, the Choi-Williams distribution, and the continuous wavelet transform were compared for estimation accuracy and precision on synthesized and real ME signals. It is found that the estimates provided by the continuous wavelet transform have better accuracy and precision than those obtained with the other time-frequency analysis methods on simulated data sets. In addition, ME signals from four subjects during three different tests (maximum static voluntary contraction, ramp contraction, and repeated isokinetic contractions) were also examined.

Method and apparatus for detection and treatment of cardiac arrhythmias

Abstract: A device for monitoring heart rhythms. The device is provided with an amplifier for receiving electrogram signals, a memory for storing digitized electrogram segments including signals indicative of depolarizations of a chamber or chamber of a patient's heart and a microprocessor and associated software for transforming analyzing the digitized signals. The digitized signals are analyzed by first transforming the signals into signal wavelet coefficients using a wavelet transform. The higher amplitude ones of the signal wavelet coefficients are identified and the higher amplitude ones of the signal wavelet coefficients are compared with a corresponding set of template wavelet coefficients derived from signals indicative of a heart depolarization of known type. The digitized signals may be transformed using a Haar wavelet transform to obtain the signal wavelet coefficients, and the transformed signals may be filtered by deleting lower amplitude ones of the signal wavelet coefficients. The transformed signals may be compared by ordering the signal and template wavelet coefficients by absolute amplitude and comparing the orders of the signal and template wavelet coefficients. Alternatively, the transformed signals may be compared by calculating distances between the signal and wavelet coefficients. In preferred embodiments the Haar transform may be a simplified transform which also emphasizes the signal contribution of the wider wavelet coefficients.

Detection and measurement of power quality disturbances using wavelet transform

Abstract: This paper deals with the use of a continuous wavelet transform to detect and analyze voltage sags and transients. A recursive algorithm is used and improved to compute the time-frequency plane of these electrical disturbances. Characteristics of investigated signals are measured on a time-frequency plane. A comparison between measured characteristics and benchmark values detects the presence of disturbances in analyzed signals and characterizes the type of disturbances. Duration and magnitude of voltage sags are measured, transients are located in the width of the signal. Furthermore, meaningful time and frequency components of transients are measured. The whole method is implemented and tested over a sample representing recorded disturbances. Detection and measurement results are compared using classical methods.

Modulation identification of digital signals by the wavelet transform

Abstract: There is a need, for example in electronic surveillance, to determine the modulation type of an incoming signal. The use of the wavelet transform for modulation identification of digital signals is described. The wavelet transform can effectively extract the transient characteristics in a digital communication signal, yielding distinct patterns for simple identification. Three identifiers for classifying PSK and FSK, M-ary PSK and M-ary FSK are considered. Statistics for hypothesis testing are derived. When the carrier-to-noise ratio is low, the symbol period and synchronisation time are needed to improve identification accuracy. A method for estimating them from the wavelet transform coefficients is included. The performance of the identifier is investigated through simulations.

Dynamic Maintenance of Wavelet-Based Histograms

Abstract: In this paper, we introduce an e cient method for the dynamic maintenance of wavelet-based histograms (and other transform-based histograms). Previous work has shown that wavelet-based histograms provide more accurate selectivity estimation than traditional histograms, such as equi-depth histograms. But since wavelet-based histograms are built by a nontrivial mathematical procedure, namely, wavelet transform decomposition, it is hard to maintain the accuracy of the histogram when the underlying data distribution changes over time. In particular, simple techniques, such as split and merge, which works well for equi-depth histograms, and updating a xed set of wavelet coe cients, are not suitable here. We propose a novel approach based upon probabilistic counting and sampling to maintain waveletbased histograms with very little online time and space costs. The accuracy of our method is robust to changing data distributions, and we get a considerable improvement over previous methods for updating transform-based histograms. A very nice feature of our method is that it can be extended naturally to maintain multidimensional wavelet-based histograms, while traditional multidimensional histograms can be less accurate and prohibitively expensive to build and maintain.

Contrast-based image fusion using the discrete wavelet transform

Abstract: We introduce a contrast-based image fusion method using the wavelet multiresolution analysis. This method includes three steps. First, the multiresolution architectures of the two original input images are obtained using the discrete wavelet transform. A new concept called directive contrast is presented. Second, the multiresolution architecture (MRA) of the fused image can be achieved by selecting the corresponding subband signals of each input image based on the directive contrast. Finally, the fused image is reconstructed using the inverse wavelet transform. This algorithm is relevant to visual sensitivity and is tested by merging visual and IR images. The result shows that the fused image can integrate the details of each original image. The visual aesthetics and the computed SNRs of the fused images show that the new approaches can provide better fusion results than some previous multiresolution fusion methods.

Evaluating arrhythmias in ECG signals using wavelet transforms

Abstract: Recent work has attempted to utilize wavelet techniques in the analysis of biomedical signals including ECGs. Here, the authors present an energy-based method of interrogating the ECG in VF using high-resolution, log-scale continuous wavelet plots. With this method, underlying structures within the VF waveform are made visible in the wavelet time-scale half space.

An Introduction to Wavelet Transform Tidal Analysis Methods

Abstract: Continuous wavelet transforms (CWTs) provide an approach to understanding the numerous tidal phenomena that deviate markedly from an assumed statistical stationarity or exact periodicity inherent in traditional tidal methods. Use of wavelets allows determination of the degree of non-stationarity present in time series, such as estuarine and shelf currents, usually treated as stationary. Wavelets also provide a consistent analysis of tidal and non-tidal variance, a feature often essential for dynamical analyses of non-stationary tides. We summarize basic notions of the wavelet transform, also known as a perfect reconstruction filter bank or a multire solution analysis, contrast them with those of harmonic analysis and Fourier transforms, construct a continuous wavelet transform basis with a scale selection especially adapted to tidal problems, describe possibilities for analysis of scalar and vector quantities, define a criterion for knowledge of independence of process between adjoining scales, and illustrate use of wavelet tools with several examples. In contrast to the nearly periodic barotropic tide typical of coastal stations, this paper analyses processes that are in part tidally driven but non-stationary, e.g. baroclinic tidal currents, river tides, continental shelf internal tides, and some kinds of biological activity in the coastal ocean. In all cases, wavelet analysis provides a consistent, linear analysis of tidal and non-tidal variance and reveals features that harmonic analysis on a Fourier transform approach could not elucidate.

Structural Damage Detection in Beams by Wavelet Transforms

Abstract: The use of a laser-based optical system and wavelet transforms is explored for the detection of changes in the properties of cantilevered aluminum beams as a result of damage. The beams were modeled using the ANSYS 5.3 finite-element method and the first six mode shapes for the damaged and the undamaged cases obtained. Damage was simulated by a reduction in the stiffness of one element. Gaussian white noise was added externally to simulate field conditions. The results show that a spatially-localized abnormality in the mode shape could be represented uniquely by a small set of wavelet coefficients while the white noise was uniformly spread throughout the wavelet space. It was observed that the damage clearly manifested in the sixth-order detail of certain modes only. A different finite-element model was used as a test beam to validate the proposed method. An actual aluminum beam, fabricated with dimensions similar to the test beam, was excited and the mode shapes recorded with the scanning laser vibrometer. Damage was created by machining a notch in the beam of the same dimensions as the finite-element test beam. An image of the damage location was obtained from the continuous wavelet transform coefficients. The magnitude of the wavelet coefficients at the damage location showed a close correlation to the severity of damage. It was observed to increase with increasing damage. The finite-element test beam results showed a close correlation to the corresponding experimental beam results. The method benefits from the fact that the undamaged mode shapes were not used to evaluate the condition of the beam, which in most field conditions is not feasible.

New Uncertainty Principles for the Continuous Gabor Transform and the Continuous Wavelet Transform

Abstract: Gabor and wavelet methods are preferred to classical Fourier methods, whenever the time dependence of the analyzed sig- nal is of the same importance as its frequency dependence. However, there exist strict limits to the maximal time-frequency resolution of these both transforms, similar to Heisenberg's uncertainty principle in Fourier analysis. Results of this type are the subject of the following article. Among else, the following will be shown: if is a window function, f 2 L 2 (R) n f0g an arbitrary signal and G f(!;t) the con- tinuous Gabor transform of f with respect to , then the support of G f(!;t) considered as a subset of the time-frequency-plane R 2 can- not possess nite Lebesgue measure. The proof of this statement, as well as the proof of its wavelet counterpart, relies heavily on the well known fact that the ranges of the continuous transforms are reproduc- ing kernel Hilbert spaces, showing some kind of shift-invariance. The last point prohibits the extension of results of this type to discrete theory.

The fractional spline wavelet transform: definition end implementation

Abstract: We define a new wavelet transform that is based on a previously defined family of scaling functions: the fractional B-splines. The interest of this family is that they interpolate between the integer degrees of polynomial B-splines and that they allow a fractional order of approximation. The orthogonal fractional spline wavelets essentially behave as fractional differentiators. This property seems promising for the analysis of 1/f/sup /spl alpha// noise that can be whitened by an appropriate choice of the degree of the spline transform. We present a practical FFT-based algorithm for the implementation of these fractional wavelet transforms, and give some examples of processing.

Identification of sources of potential fields with the continuous wavelet transform: Complex wavelets and application to aeromagnetic profiles in French Guiana

Abstract: A continuous wavelet technique has been recently introduced to analyze potential fields data First, we summarize the theory, which primarily consists of interpreting potential fields via the properties of the upward continued derivative field Using complex wavelets to analyze magnetic data gives an inverse scheme to find the depth and homogeneity degree of local homogeneous sources and the inclination of their magnetization vector This is analytically applied on several local and extended synthetic magnetic sources The application to other potential fields is also discussed Then, profiles crossing dikes and faults are extracted from the recent high-resolution aeromagnetic survey of French Guiana and analyzed using complex one dimensional wavelets Maps of estimated depth to sources and their magnetization inclination and homogeneity degree are proposed for a region between Cayenne and Kourou

Wavelet analysis of transient biomedical signals and its application to detection of epileptiform activity in the EEG.

Abstract: Wavelet based signal analysis provides a powerful new means for the analysis of nonstationary signals such as the human EEG. The properties of the discrete wavelet transform are reviewed in illustrated application examples. The continuous wavelet transform is shown to provide better detection and representation of isolated transients. An approach to extract features of edges and transients from the continuous wavelet transform is outlined. Matching pursuit is presented as a more general transform method that covers both transients and oscillation spindles. A statistical model for the continuous wavelet transform of background EEG is found. A spike detection system based on this background model is presented. The performance of this detection system has been assessed in a preliminary clinical study of 11 EEG recordings containing epileptiform activity and shown to have a sensitivity of 84% and a selectivity of 12%. The spatial context of epileptiform activity will be incorporated to improve system performance.

A characterization of wavelets on general lattices

Abstract: In the context of a general lattice Γ in Rn and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families. This result generalizes the characterization of Frazier, Garrigos, Wang, and Weis about the wavelet families with Γ = Zn and M = 21. In the second part of the paper, we characterize all the MSF wavelets. Moreover, we give a constructive method for the support of the Fourier transform of an MSF wavelet and apply this method by giving examples with particular attention to the quincunx lattice.

A new motion parameter estimation algorithm based on the continuous wavelet transform

Abstract: This paper presents a novel motion parameter estimation (ME) algorithm based on the spatio-temporal continuous wavelet transform (CWT). The multidimensional nature of the CWT allows for the definition of a multitude of energy densities by integrating over a subset of the CWT parameter space. Three energy densities are used to estimate motion parameters by sequentially optimizing a state vector composed of velocity, position, and size parameters. This optimization is performed on a frame-by-frame basis allowing the algorithm to track moving objects. The ME algorithm is designed to address real world challenges encountered in the defense industry and traffic monitoring scenarios, such as attaining robust performance in noise and handling obscuration and crossing object trajectories.

Generalized fourier transform processing system

Abstract: Improved Fourier transform processing systems for a data transmission system are disclosed. The improved Fourier transform processing systems efficiently performs Fourier transform signal processing. In addition, the improved Fourier transform processing can perform address transformations to better and more efficiently use a memory system for in-place processing. The address transformations are provided by a generalized address translation algorithm that works for any size Fourier transform, in any radix, and with various memory architectures. The processing system can also be pipelined. The invention is particularly well suited for performing in-place processing in a data transmission system.

A multiresolution approach to spike detection in EEG

Abstract: A technique is proposed for the automatic detection of spikes in electroencephalograms (EEG). A multiresolution approach and a non-linear energy operator are exploited. The signal on each EEG channel is decomposed into three subbands using a non-decimated wavelet transform. Each subband is analyzed by using a non-linear energy operator, in order to detect peaks. A decision rule detects the presence of spikes in the EEG, relying upon the energy of the three subbands. The effectiveness of the proposed technique was confirmed by analyzing both test signals and EEG layouts.

Clifford-Hermite Wavelets in Euclidean Space

Abstract: Specific kernel functions for the continuous wavelet transform in higher dimension and new continuous wavelet transforms are presented within the framework of Clifford analysis. Their relationship with the heat equation and the newly introduced wavelet differential equation is established.

The Condition Monitoring of Diesel Engines Using Acoustic Measurements-Part 2: Fault Detection and Diagnosis

Abstract: In this paper, the focus is upon the condition monitoring implications of acoustic monitoring Namely, its ability to detect, diagnose and locate incipient deterioration in a number of common failure modes To improve the reliability of the condition monitoring procedures, the noise contaminated signals are conditioned based upon the results of speed and load dependency investigation of the identified low and high frequency regions of sound High pass filtering is shown to eliminate much of the environmental dependency of the monitored signals, whilst retaining the pertinent condition indicating information content Real fault testing shows that the location of different faults, their influences upon combustion, and the ability to distinguish between them can all be extracted from the shape of the contours in the Continuous Wavelet Transform (CWT) The sister paper to this (""Part 1 - Acoustic Characteristics of the Engine and Representation of the Acoustic Signals""), the sound generation of a diesel engine is modelled based upon the combustion process Real monitored data is shown to be highly contaminated, and the representation of acoustic signals using the smoothed pseudo-Wigner-Ville distribution (SPWVD) and continuous wavelet transform (CWT), however, is found to permit recognition of the adverse influences of the measurement environment

Wavelet-based algorithm for voltage flicker analysis

Abstract: Fourier transform-based algorithms have been popular for voltage flicker analysis; however, their accuracy is unfavorably influenced by the leakage effect. This paper presents a wavelet-based algorithm for voltage flicker analysis. The algorithm can accurately extract the voltage flicker components by the direct demodulation of the voltage signal. The performance characteristics of the algorithm are evaluated with examples of appropriate simulated and field data. The results illustrate the proposed algorithm is free of leakage effect problems.

Application of Wavelet Transforms to Reservoir-Data Analysis and Scaling

Abstract: General characterization of physical systems uses two aspects of data analysis methods: decomposition of empirical data to determine model parameters and reconstruction of the image using these characteristic parameters. Spectral methods, involving a frequency based representation of data, usually assume stationarity. These methods, therefore, extract only the average information and hence are not suitable for analyzing data with isolated or deterministic discontinuities, such as faults or fractures in reservoir rocks or image edges in computer vision. Wavelet transforms provide a multiresolution framework for data representation. They are a family of orthogonal basis functions that separate a function or a signal into distinct frequency packets that are localized in the time domain. Thus, wavelets are well suited for analyzing non-stationary data. In other words, a projection of a function or a discrete data set onto a time-frequency space using wavelets shows how the function behaves at different scales of measurement. Because wavelets have compact support, it is easy to apply this transform to large data sets with minimal computations. We apply the wavelet transforms to one-dimensional and two-dimensional permeability data to determine the locations of layer boundaries and other discontinuities. By binning in the time-frequency plane with wavelet packets, permeability structuresmore » of arbitrary size are analyzed. We also apply orthogonal wavelets for scaling up of spatially correlated heterogeneous permeability fields.« less

New lifting based structure for undecimated wavelet transform

Abstract: A new structure for the undecimated wavelet transform (UWT) is introduced. This structure combines the stationary wavelet transform with a lifting scheme and its design is based on a polyphase structure. The suggested structure inherits the simplicity of the lifting scheme, such that the inverse transform is easily implemented. The proposed performance of the UWT is verified on a signal denoising application.

Fast spatial combinative lifting algorithm of wavelet transform using the 9/7 filter for image block compression

Abstract: A new fast spatial combinative lifting algorithm (SCLA) of the wavelet transform using the 9/7 filter for image block compression is proposed. In comparison with its lifting-based implementation, the number of multiplications is reduced by a ratio of 5/12 and the speed of implementation of the wavelet transform is increased.

The detection of echoes from multilayer structures using the wavelet transform

Abstract: A method for measuring unknown thicknesses of multilayer structures, based on echo detection by means of the wavelet transform (WT), is presented. A brief discussion of the theoretical considerations underlying the method is first given. This highlights the excellent performance shown by the WT as a powerful tool for the analysis of echoes in a noisy environment. A suitable operating procedure for validation of the method is then set up. To this end, tests on 1) simulated signals and 2) actual signals received from known thicknesses are carried out: the obtained results are finally given and discussed.