Wavelet Analysis

Musical genres are categorical labels created by humans to characterize pieces of music. A musical genre is characterized by the common characteristics shared by its members. These characteristics typically are related to the instrumentation, rhythmic structure, and harmonic content of the music. Genre hierarchies are commonly used to structure the large collections of music available on the Web. Currently musical genre annotation is performed manually. Automatic musical genre classification can assist or replace the human user in this process and would be a valuable addition to music information retrieval systems. In addition, automatic musical genre classification provides a framework for developing and evaluating features for any type of content-based analysis of musical signals.

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes. Annu. Rev. Fluid. Mech. 1999.31:417-457. Downloaded from arjournals.annualreviews.org by CALIFORNIA INSTITUTE OF TECHNOLOGY on 09/08/05. For personal use only.

Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by de ning a type of translation invariance that we call \shiftability". In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are speci ed by the sampling theorem. Shiftability may also be considered in the context of other domains, particularly orientation and scale. We explore \jointly shiftable" transforms that are simultaneously shiftable in more than one domain. Two examples of jointly shiftable transforms are designed and implemented: a one-dimensional transform that is jointly shiftable in position and scale, and a two-dimensional transform that is jointly shiftable in position and orientation. We demonstrate the usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement.

The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in the time-frequency plane, each of which can be viewed as approximately harmonic locally, with slowly varying amplitudes and frequencies. The EMD has already shown its usefulness in a wide range of applications including meteorology, structural stability analysis, medical studies. On the other hand, the EMD algorithm contains heuristic and ad hoc elements that make it hard to analyze mathematically. In this paper we describe a method that captures the flavor and philosophy of the EMD approach, albeit using a different approach in constructing the components. The proposed method is a combination of wavelet analysis and reallocation method. We introduce a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and we prove that our method does indeed succeed in decomposing arbitrary functions in this class. We provide several examples, for simulated as well as real data.

A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational, and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long-range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono versus multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.

This correspondence introduces a new approach to characterize textures at multiple scales. The performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classification of twenty-five natural textures. Both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations, where each wavelet packet (channel) reflected a specific scale and orientation sensitivity. Wavelet packet representations for twenty-five natural textures were classified without error by a simple two-layer network classifier. An analyzing function of large regularity ( 0 2 0 ) was shown to be slightly more efficient in representation and discrimination than a similar function with fewer vanishing moments (Ds). In addition, energy representations computed from the standard wavelet decomposition alone (17 features) provided classification without error for the twenty-five textures included in our study. The reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are beneficial for accomplishing segmentation, classification and subtle discrimination of texture.

In dimensions two and higher, wavelets can efficiently represent only a small range of the full diversity of interesting behavior. In effect, wavelets are welladapted for pointlike phenomena, whereas in dimensions greater than one, interesting phenomena can be organized along lines, hyperplanes, and other nonpointlike structures, for which wavelets are poorly adapted.

The kurtogram is a fourth-order spectral analysis tool recently introduced for detecting and characterising nonstationarities in a signal. The paradigm relies on the assertion that each type of transient is associated with an optimal (frequency/frequency resolution) dyad {f ; Df } which maximises its kurtosis, and hence its detection. However, the complete exploration of the whole plane (f ; Df ) is a formidable task hardly amenable to on-line industrial applications. In this communication we describe a fast algorithm for computing the kurtogram over a grid that finely samples the (f ; Df ) plane. Its complexity is on the order of N log N, similarly to the FFT. The efficiency of the algorithm is then illustrated on several industrial cases concerned with the detection of incipient transient faults. r Fig. 2. Fast kurtogram paving of the (frequency/frequency resolution) plane. J. Antoni / Mechanical Systems and Signal Processing ] (]]]]) ]]]-]]]

We introduce a metric for probability distributions, which is bounded, information-theoretically motivated, and has a natural Bayesian interpretation. The square root of the well-known distance is an asymptotic approximation to it. Moreover, it is a close relative of the capacitory discrimination and Jensen-Shannon divergence.

The vibration signals of a machine always carry the dynamic information of the machine. These signals are very useful for the feature extraction and fault diagnosis. However, in many cases, because these signals have very low signal-to-noise ratio (SNR), to extract feature components becomes di$cult and the applicability of information drops down. Wavelet analysis in an e!ective tool for signal processing and feature extraction. In this paper, a denoising method based on wavelet analysis is applied to feature extraction for mechanical vibration signals. This method is an advanced version of the famous &&soft-thresholding denoising method'' proposed by Donoho and Johnstone. Based on the Morlet wavelet, the time-frequency resolution can be adapted to di!erent signals of interest. In this paper, this denoising method is introduced in detail. The results of the application in rolling bearing diagnosis and gear-box diagnosis are satisfactory.

We study the application of the Bamberger directional filter bank to the problem of rotation invariant texture classification. We explore the use of purely directional decompositions and the use of polar-separable Bamberger pyramids. We obtain comparable classification performance to Gabor-based methods using a smaller feature set.

This paper compares two general and formal solutions to the problem of fusion of multispectral images with high-resolution panchromatic observations. The former exploits the undecimated discrete wavelet transform, which is an octave bandpass representation achieved from a conventional discrete wavelet transform by omitting all decimators and upsampling the wavelet filter bank. The latter relies on the generalized Laplacian pyramid, which is another oversampled structure obtained by recursively subtracting from an image an expanded decimated lowpass version. Both the methods selectively perform spatial-frequencies spectrum substitution from an image to another. In both schemes, context dependency is exploited by thresholding the local correlation coefficient between the images to be merged, to avoid injection of spatial details that are not likely to occur in the target image. Unlike other multiscale fusion schemes, both the present decompositions are not critically subsampled, thus avoiding possible impairments in the fused images, due to missing cancellation of aliasing terms. Results are presented and discussed on SPOT data.

This paper describes the use of wavelet transform for analyzing power system fault transients in order to determine the fault location. Traveling wave theory is utilized in capturing the travel time of the transients along the monitored lines between the fault point and the relay. Time resolution for the high frequency components of the fault transients, is provided by the wavelet transform. This information is related to the travel time of the signals which are already decomposed into their modal components. Aerial mode is used for all fault types, whereas the ground mode is used to resolve problems associated with certain special cases. Wavelet transform is found to be an excellent discriminant for identifying the traveling wave reflections from the fault irrespective of the fault type and impedance. EMTP simulations are used to test and validate the proposed fault location approach for typical power system faults.

Schizophrenia has been conceptualized as a failure of cognitive integration, and abnormalities in neural circuitry (particularly inhibitory interneurons) have been proposed as a basis for this disorder. We used measures of phase locking and phase coherence in the scalp-recorded electroencephalogram to examine the synchronization of neural circuits in schizophrenia. Compared with matched control subjects, schizophrenia patients demonstrated: (1) absence of the posterior component of the early visual gamma band response to Gestalt stimuli; (2) abnormalities in the topography, latency, and frequency of the anterior component of this response; (3) delayed onset of phase coherence changes; and (4) the pattern of anterior-posterior coherence increases in response to Gestalt stimuli found in controls was replaced by a pattern of interhemispheric coherence decreases in patients. These findings support the hypothesis that schizophrenia is associated with impaired neural circuitry demonstrate...

Our goal in this paper is to show that many of the tools of signal processing, adapted Fourier and wavelet analysis can be naturally lifted to the setting of digital data clouds, graphs and manifolds. We use diffusion as a smoothing and scaling tool to enable coarse graining and multiscale analysis. Given a diffusion operator T on a manifold or a graph, with large powers of low rank, we present a general multiresolution construction for efficiently computing, representing and compressing T t . This allows a direct multiscale computation, to high precision, of functions of the operator, notably the associated Green's function, in compressed form, and their fast application. Classes of operators for which these computations are fast include certain diffusion-like operators, in any dimension, on manifolds, graphs, and in non-homogeneous media. We use ideas related to the Fast Multipole Methods, and to the wavelet analysis of Calderón-Zygmund and pseudodifferential operators, to numerically enforce the emergence of a natural hierarchical coarse graining of a manifold, graph or data set. For example for a body of text documents the construction leads to a directory structure at different levels of generalization. The dyadic powers of an operator can be used to induce a multiresolution analysis, as in classical Littlewood-Paley and wavelet theory: we construct, with efficient and stable algorithms, bases of orthonormal scaling functions and wavelets associated to this multiresolution analysis, together with the corresponding downsampling operators, and use them to compress the corresponding powers of the operator. While most of our discussion deals with symmetric operators and relates to localization to spectral bands, the symmetry of the operators and their spectral theory need not be considered, as the main assumption is reduction of the numerical ranks as we take powers of the operator.

The assessment of the comovement among international stock markets is of key interest, for example, for the international portfolio diversification literature. In this paper, we re-examine such comovement by resorting to a novel approach, wavelet analysis. Wavelet analysis allows one to measure the comovement in the time–frequency space. In this way, one can characterize how international stock returns relate in

Ongoing global climatic change initiated by the anthropogenic release of carbon dioxide is a matter of intense debate. We focus both on the impact of these climatic changes on the global hydrological cycle and on the amplitude of the increase of global and continental runoff over the last century, in relation to measured temperature increases. In this contribution, we propose an original statistical wavelet-based method for the reconstruction of the monthly discharges of worldwide largest rivers. This method provides a data-based approximation of the evolution of the annual continental and global runoffs over the last century. A consistent correlation is highlighted between global annual temperature and runoff, suggesting a 4% global runoff increase by 1°C global temperature rise. However, this global trend should be qualified at the regional scale where both increasing and decreasing trends are identified. North America runoffs appear to be the most sensitive to the recent climatic changes. Finally, this contribution provides the first experimental data-based evidence demonstrating the link between the global warming and the intensification of the global hydrological cycle. This corresponds to more intense evaporation over oceans coupled to continental precipitation increase or continental evaporation decrease. This process finally leads to an increase of the global continental runoff.

In literature, several methods are available to combine both low spatial multispectral and low spectral panchromatic resolution images to obtain a high resolution multispectral image. One of the most common problems encountered in these methods is spectral distortions introduced during the merging process. At the same time, the spectral quality of the image is the most important factor affecting the accuracy of the results in many applications such as object recognition, object extraction, image analysis. In this study, the most commonly used methods including GIHS, GIHSF, PCA and Wavelet are analyzed using image quality metrics such as SSIM, ERGAS and SAM. At the same time, Wavelet is the best method for obtaining the fused image having the least spectral distortions according to obtained results. At the same time, image quality of GIHS, GIHSF and PCA methods are close to each other, but spatial qualities of the fused image using the wavelet method are less than others.

This paper describes a video coding system based on motion-compensated three-dimensional (3-D) subband/wavelet coding (MC-3DSBC), which can overcome the limits of both 3-D SBC and MC prediction-based coding. In this new system, spatiotemporal subbands are generated by MC temporal analysis and a spatial wavelet transform, and then encoded by 3-D subbandfinite state scalar quantization (3DSB-FSSQ). The rate allocation from the GOP level to each class of subbands is optimized by utilizing the structural property of MC-3DSBC that additive superposition approximately holds for both rate and distortion. The proposed video coding system is applied to several test video clips. Its performance exceeds that of both a known MPEG-1 implementation and a similar subband MC predictive coder while maintaining modest computational complexity and memory size.

This paper is a comparative study of three recently proposed algorithms for face recognition: eigenface, autoassociation and classification neural nets, and elastic matching. After these algorithms were analyzed under a common statistical decision framework, they were evaluated experimentally on four individual data bases, each with a moderate subject size, and a combined data base with more than a hundred different subjects. Analysis and experimental results indicate that the eigenface algorithm, which is essentially a minimum distance classifier, works well when lighting variation is small. Its performance deteriorates significantly as lighting variation increases. The elastic matching algorithm, on the other hand, is insensitive to lighting, face position, and expression variations and therefore is more versatile. The performance of the autoassociation and classification nets is upper bounded by that of the eigenface but is more difficult to implement in practice.

Wavelet analysis is a powerful tool that is already in use throughout science and engineering. The versatility and attractiveness of the wavelet approach lie in its decomposition properties, principally its time-scale localization. It is especially relevant to the analysis of nonstationary systems, i.e., systems with short-lived transient components, like those observed in ecological systems. Here, we review the basic properties of the wavelet approach for time-series analysis from an ecological perspective. Wavelet decomposition offers several advantages that are discussed in this paper and illustrated by appropriate synthetic and ecological examples. Wavelet analysis is notably free from the assumption of stationarity that makes most methods unsuitable for many ecological time series. Wavelet analysis also permits analysis of the relationships between two signals, and it is especially appropriate for following gradual change in forcing by exogenous variables.

This contribution provides a review of the most recent wavelet applications in the field of earth sciences and is devoted to introducing and illustrating new wavelet analysis methods in the field of hydrology. Wavelet analysis remains unknown in the field of hydrology even though it clearly overcomes the well-known limits of the classical Fourier analysis. New wavelet-based tools are proposed to hydrologists in order to make wavelet analysis more attractive. First, a multiresolution continuous wavelet analysis method is shown to significantly improve the determination of the temporal-scale structure of a given signal. Second, the concept of wavelet entropy in both continuous and multiresolution frameworks is introduced allowing for an estimation of the temporal evolution of a given hydrological or climatologic signal's complexity. New insights in the scale-dependence of the relationship are exposed by introducing wavelet cross-correlation and wavelet coherence. Continuous wavelet cross-correlation provides a time-scale distribution of the correlation between two signals, whereas continuous wavelet coherence provides a qualitative estimator of the temporal evolution of the degree of linearity of the relationship between two signals on a given scale. These methods are applied to four large river runoffs and two global climatic indexes in a companion paper. q

Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. This paper proposes a novel Bayesian-based algorithm within the framework of wavelet analysis, which reduces speckle in SAR images while preserving the structural features and textural information of the scene. First, we show that the subband decompositions of logarithmically transformed SAR images are accurately modeled by alpha-stable distributions, a family of heavy-tailed densities. Consequently, we exploit this a priori information by designing a maximum a posteriori (MAP) estimator. We use the alpha-stable model to develop a blind speckle-suppression processor that performs a nonlinear operation on the data and we relate this nonlinearity to the degree of non-Gaussianity of the data. Finally, we compare our proposed method to current state-of-the-art soft thresholding techniques applied on real SAR imagery and we quantify the achieved performance improvement.

This article, written in honor of Professor Nemat-Nasser, provides an update of the standard theories of dislocation dynamics, plasticity and elasticity properly modified to include scale effects through the introduction of higher order spatial gradients of constitutive variables in the governing equations of material description. Only a special class of gradient models, namely those developed by the author and his co-workers, are considered. After a brief review of the basic mathematical structure of the theory and certain gradient elasticity solutions for dislocation fields, the physical origin and form of the gradient terms (for all classes of elastic, plastic, and dislocation dynamics behavior), along with the nature of the associated phenomenological coefficients are discussed. Applications to the interpretation of deformation patterning and size effects are given. Two new features are noted: the role of wavelet analysis and stochasticity in interpreting deformation heterogeneity measurements and serrations of the stress-strain graph.

This paper presents a new approach for power quality analysis using a modified wavelet transform known as S-transform. The local spectral information of the wavelet transform can, with slight modification, be used to perform local cross spectral analysis with very good time resolution. The 'phase correction' absolutely references the phase of the wavelet transform to the zero time point, thus assuring that the amplitude peaks are regions of stationary phase. The excellent time-frequency resolution characteristic of the S-transform makes it an attractive candidate for analysis of power system disturbance signals. Several power quality problems are analysed using both the S-transform and discrete wavelet transform, showing clearly the advantage of the S-transform in detecting, localizing and classifying the power quality problems.

The flow of energy through the solar atmosphere and the heating of the Sun's outer regions are still not understood. Here, we report the detection of oscillatory phenomena associated with a large bright-point group that is 430,000 square kilometers in area and located near the solar disk center. Wavelet analysis reveals full-width half-maximum oscillations with periodicities ranging from 126 to 700 seconds originating above the bright point and significance levels exceeding 99%. These oscillations, 2.6 kilometers per second in amplitude, are coupled with chromospheric line-of-sight Doppler velocities with an average blue shift of 23 kilometers per second. A lack of cospatial intensity oscillations and transversal displacements rules out the presence of magneto-acoustic wave modes. The oscillations are a signature of Alfvén waves produced by a torsional twist of ±22 degrees. A phase shift of 180 degrees across the diameter of the bright point suggests that these torsional Alfvén oscillations are induced globally throughout the entire brightening. The energy flux associated with this wave mode is sufficient to heat the solar corona.

In the context of image coding, a number of reversible integer-to-integer wavelet transforms are compared on the basis of their lossy compression performance, lossless compression performance, and computational complexity. Of the transforms considered, several were found to perform particularly well, with the best choice for a given application depending on the relative importance of the preceding criteria. Reversible integer-to-integer versions of numerous transforms are also compared to their conventional (i.e., non-reversible real-to-real) counterparts for lossy compression. At low bit rates, reversible integer-to-integer and conventional versions of transforms were found to often yield results of comparable quality. Factors affecting the compression performance of reversible integer-to-integer wavelet transforms are also presented, supported by both experimental data and theoretical arguments.

Karstic watersheds appear as highly as non-linear and non-stationary systems. The behaviour of karstic springs has been previously studied using non-linear simulation methods (Volterra expansion) and non-stationary analyses methods based on wavelet transforms. The main issue of karstic spring behaviour consists of the presence and the identi®cation of characteristic time-scales.

This paper presents a nontechnical, conceptually oriented introduction to wavelet analysis and its application to neuroelectric waveforms such as the EEG and event related potentials (ERP). Wavelet analysis refers to a growing class of signal processing techniques and transforms that use wavelets and wavelet packets to decompose and manipulate time-varying, nonstationary signals. Neuroelectric waveforms fall into this category of signals because they typically have frequency content that varies as a function of time and recording site. Wavelet techniques can optimize the analysis of such signals by providing excellent joint time-frequency resolution. The ability of wavelet analysis to accurately resolve neuroelectric waveforms into specific time and frequency components leads to several analysis applications. Some of these applications are time-varying filtering for denoising single trial ERPs, EEG spike and spindle detection, ERP component separation and measurement, hearingthreshold estimation via auditory brainstem evoked response measurements, isolation of specific EEG and ERP rhythms, scale-specific topographic analysis, and This work was conducted in the course of an agreement with the U.S. Department of Education. We are grateful to Henri Begleiter, Walter Pritchard, and Don Tucker for providing us with neuroelectric data sets. We also greatly appreciate the helpful coments of Padmanabhan Sudevan on an earlier draft of this manuscript.

Support vector machine (SVM) is an extensively used machine learning method with many biomedical signal classification applications. In this study, a novel PSO-SVM model have been proposed that hybridized the particle swarm optimization (PSO) and SVM to improve the EMG signal classification accuracy. This optimization mechanism involves kernel parameter setting in the SVM training procedure, which significantly influences the classification accuracy. The experiments were conducted on the basis of EMG signal to classify into normal, neurogenic or myopathic. In the proposed method the EMG signals were decomposed into the frequency sub-bands using discrete wavelet transform (DWT) and a set of statistical features was extracted from these sub-bands to represent the distribution of wavelet coefficients. The obtained results obviously validate the superiority of the SVM method compared to conventional machine learning methods, and suggest that further significant enhancements in terms of classification accuracy can be achieved by the proposed PSO-SVM classification system. The PSO-SVM yielded an overall accuracy of 97.41% on 1200 EMG signals selected from 27 subject records against 96.75%, 95.17% and 94.08% for the SVM, the k-NN and the RBF classifiers, respectively. PSO-SVM is developed as an efficient tool so that various SVMs can be used conveniently as the core of PSO-SVM for diagnosis of neuromuscular disorders.

Due to the importance of rolling bearings as one of the most widely used industrial machinery elements, development of proper monitoring and fault diagnosis procedure to prevent malfunctioning and failure of these elements during operation is necessary. For rolling bearing fault detection, it is expected that a desired time-frequency analysis method has good computational efficiency, and has good resolution in both, time and frequency domains. The point of interest of this investigation is the presence of an effective method for multi-fault diagnosis in such systems with optimizing signal decomposition levels by using wavelet analysis and support vector machine (SVM). The system that is under study is an electric motor which has two rolling bearings, one of them is next to the output shaft and the other one is next to the fan and for each of them there is one normal form and three false forms, which make 8 forms for study. The results that we achieved from wavelet analysis and SVM are fully in agreement with empirical result. r

The aim of this paper is to examine a set of wavelet functions (wavelets) for implementation in a still image compression system and to highlight the benefit of this transform relating to today's methods. The paper discusses important features of wavelet transform in compression of still images, including the extent to which the quality of image is degraded by the process of wavelet compression and decompression. Image quality is measured objectively, using peak signal-to-noise ratio or picture quality scale, and subjectively, using perceived image quality. The effects of different wavelet functions, image contents and compression ratios are assessed. A comparison with a discrete-cosine-transform-based compression system is given. Our results provide a good reference for application developers to choose a good wavelet compression system for their application.

Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced.

A new methodology for fusing satellite sensor imagery, based on tailored filtering in the Fourier domain is proposed. Finite-duration Impulse Response (FIR) filters have been designed through an objective criterion, which depends on source image characteristics only. The designed filters allow a weighted fusion of the information contained in a fine spatial resolution image (PAN) and in a multispectral image (MULTI), respectively, establishing a trade-off between spatial and spectral quality of the resulting fused image. This new technique has been tested with Landsat Enhanced Thematic Mapper Plus (ETM+) imagery. Spatial and spectral quality of the fused images was compared with the results provided by Mallat's Wavelet algorithm. The images fused by the proposed method were characterized by a spatial resolution very close to the PAN image, and by the spectral resolution of the MULTI image.

Over the last few decades, the damage identification methods of civil and mechanical structures have been drawing much interest from various fields. Wavelet analysis, a relatively new mathematical and signal processing tool, is one of such methods that has been studied recently. It is a time-frequency analysis that provides more detailed information about non-stationary signals which traditional Fourier analysis miss. This rather new method has been applied to various fields including civil, mechanical and aerospace engineering, especially for damage detection and structural health monitoring (SHM). The purpose of this paper is to provide the review of the research that has been conducted on damage detection by wavelet analysis. First, the theory of wavelet analysis is presented including continuous and discrete wavelet transform followed by its application to SHM. Then more specific applications-namely crack detection of a beam and mechanical gear and roller damage-are presented. #

Annual maximum streamflow and annual maximum water level and their variations exert most serious influences on human society. In this paper, temporal trends and frequency changes at three major stations of Yangtze River, i.e. Yichang, Hankou and Datong representing upper, middle and lower reaches, respectively, were detected with the help of parametric t-test, Mann-Kendall (MK) analysis and wavelet transform methods. The results show that: (1) there is a significant upward trend in streamflow at middle Yangtze River, indicating that flood hazard in the middle reach of the river, the flood rich region, will be more serious; (2) there is a consistent increase of water level from upper to lower reaches of the river which does not always coincide with the maximum streamflow variations; and (3) the periods of water level changes are decreasing over time, indicating the increasing occurrence frequency of annual maximum water level over time. This phenomenon is more obvious from upper Yangtze River to the lower Yangtze River. Human activities like destruction of vegetation, land reclamation and construction of levees reduced lake sizes and filled up the river bed, reducing the flood storage capacity of lakes and fluvial channel. These factors led to higher water level even some times the streamflow is small. Human should adjust his activity to enhance his adaptive capacity to flood hazard in the future. q

In this work we studied and validated a simple heartbeat classifier based on ECG feature models selected with the focus on an improved generalization capability. We considered features from the RR series, as well as features computed from the ECG samples and different scales of the wavelet transform, at both available leads. The classification performance and generalization were studied using publicly available databases: the MIT-BIH Arrhythmia, the MIT-BIH Supraventricular Arrhythmia and the St. Petersburg Institute of Cardiological Technics (INCART) databases. The Association for the Advancement of Medical Instrumentation (AAMI) recommendations for class labeling and results presentation were followed. A floating feature selection algorithm was used to obtain the best performing and generalizing models in the training and validation sets for different search configurations. The best model found comprehends 8 features, was trained in a partition of the MIT-BIH Arrhythmia, and was evaluated in a completely disjoint partition of the same database. The results obtained were: global accuracy of 93%; for normal beats, sensitivity (S) 95%, positive predictive value (P + ) 98%; for supraventricular beats, S 77%, P + 39%; for ventricular beats S 81%, P + 87%. In order to test the generalization capability, performance was also evaluated in the INCART, with results comparable to those obtained in the test set. This classifier model has fewer features and performs better than other state of the art methods with results suggesting better generalization capability.

In previous works ([9-10]), the authors proposed a novel method for the diagnosis of rotor bar failures in induction machines, based on the analysis of the startup stator current through the Discrete Wavelet Transform (DWT). In those works the physical basis of the method was described and several verifications were done in order to confirm its validity. These verifications were satisfactory, but they were based on numerical simulations and on several tests that were developed using a laboratory machine, with certain particular constructive characteristics, different from those of the commercial motors. In the paper to be presented, the validity of the new diagnosis method is checked using a set of commercial induction motors. Several experiments are developed under different cases (healthy machine and machine with different levels of failure) and operating conditions (no load, full-load, pulsating load and fluctuating voltage). In each case, the results are compared with those obtained using the classical approach, based on the analysis of the steady-state current using the Fourier Transform. Finally, the results are discussed and some considerations about the influence of the DWT parameters (type of mother wavelet, order of the mother wavelet, sampling rate or number of levels of the decomposition) over the diagnosis are done.

In the current context of global infectious disease risks, a better understanding of the dynamics of major epidemics is urgently needed. Time-series analysis has appeared as an interesting approach to explore the dynamics of numerous diseases. Classical time-series methods can only be used for stationary time-series (in which the statistical properties do not vary with time). However, epidemiological time-series are typically noisy, complex and strongly non-stationary. Given this specific nature, wavelet analysis appears particularly attractive because it is well suited to the analysis of non-stationary signals. Here, we review the basic properties of the wavelet approach as an appropriate and elegant method for timeseries analysis in epidemiological studies. The wavelet decomposition offers several advantages that are discussed in this paper based on epidemiological examples. In particular, the wavelet approach permits analysis of transient relationships between two signals and is especially suitable for gradual change in force by exogenous variables.

Instrumental station pressure, temperature and precipitation measurements and proxy data were used to statistically reconstrud monthly time series of the North Atlantic Oscillation (NAO) and the Eurasian (EU) circulation indices back to 1675. Systematic testing of the reconstruction procedure indicated generally reliable reconstructions throughout the entire period, except for summertime before about 1750. Predictive skill varied for different sub-periods depending on data availability. It was highest for autumn and winter and was generally better for the EU than for the NAO index. Wavelet analysis suggested significant low-frequency variability, especially for the spring, summer and annual averaged indices, The co-variability between the NAO and EU indices was found to exhibit large decadal to century timescale variations, indicating that climate variabjJjty over the continent is temporarily decoupled from the NAO,

The analysis, identification, characterization and simulation of random processes utilizing both the continuous and discrete wavelet transform is addressed. The wavelet transform is used to decompose random processes into localized orthogonal basis functions, providing a convenient format for the modeling, analysis, and simulation of non-stationary processes. The time and frequency analysis made possible by the wavelet transform provides insight into the character of transient signals through time-frequency maps of the time variant spectral decomposition that traditional approaches miss. In the relatively short life of the wavelet transform, it has found use in a wide variety of applications. This applications-orientated paper will briefly discuss the development of the continuous and discrete wavelet transform for digital signal analysis and present numerous examples where the authors have found wavelet analysis useful in their studies concerning the identification and characterization of transient random processes involving ocean engineering, wind and earthquakes.

Without a doubt the first step in any water resources management is the rainfall-runoff modeling over the watershed. However considering high stochastic property of the process, many models are being still developed in order to define such a complex phenomenon in the field of hydrologic engineering. Recently Artificial Neural Network (ANN) as a non-linear inter-extrapolator is extensively used by hydrologists for rainfall-runoff modeling as well as other fields of hydrology. In the current research, the wavelet analysis was linked to the ANN concept for modeling Ligvanchai watershed rainfall-runoff process at Tabriz, Iran. For this purpose the main time series of two variables, rainfall and runoff, were decomposed to some multi-frequently time series by wavelet theory, then these time series were imposed as input data to the ANN to predict the runoff discharge 1 day ahead. The obtained results show the proposed model can predict both short and long term runoff discharges because of using multi-scale time series of rainfall and runoff data as the ANN input layer.

Compressed sensing (CS) is an emerging signal processing paradigm that enables sub-Nyquist processing of sparse signals such as electrocardiogram (ECG) and electromyogram (EMG) biosignals. Consequently, it can be applied to biosignal acquisition systems to reduce the data rate to realize ultra-low-power performance. CS is compared to conventional and adaptive sampling techniques and several system-level design considerations are presented for CS acquisition systems including sparsity and compression limits, thresholding techniques, encoder bit-precision requirements, and signal recovery algorithms. Simulation studies show that compression factors greater than 16X are achievable for ECG and EMG signals with signal-to-quantization noise ratios greater than 60 dB.