Wavelet Analysis

The mid-Pleistocene transition (MPT) from obliquity-to eccentricity-forced climate variations has been extensively documented within the oceanic realm. Using a collection of orbitally tuned records of palaeoclimatic change from the loess sequences of northern China, we have analysed terrestrial palaeomonsoon behaviour since 1.5 Ma and characterised the structure of the MPT. Wavelet analysis of a stacked magnetic susceptibility record from the loess sequences indicates that the onset of 100-kyr cyclicity was synchronous in both global ice volume and the East Asian monsoon system. However, analysis in the time domain reveals that during the MPT 'interim' period the East Asian winter monsoon appears to have weakened whilst global ice volume was increasing, indicating that the palaeomonsoon was not the primary forcing mechanism responsible for driving the global climatic change.

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.

This paper presents a comparative performance analysis of various trend detection methods developed using fuzzy logic, statistical, regression, and wavelet techniques. The main contribution of this paper is the introduction of a new method that uses noise rejection fuzzy clustering to enhance the performance of trend detection methodologies. Furthermore, another contribution of this work is a comparative investigation that produced systematic guidelines for the selection of a proper trend detection method for different application requirements. Examples of representative physiological variables considered in this paper to examine the trend detection algorithms are: 1) blood pressure signals (diastolic and systolic); and 2) heartbeat rate based on RR intervals of electrocardiography signal. Furthermore, synthetic physiological data intentionally contaminated with various types of real-life noise has been generated and used to test the performance of trend detection methods and develop noise-insensitive trend-detection algorithms.

In this paper, we describe an intelligent signal analysis system employing the wavelet transformation towards solving vehicle engine diagnosis problems. Vehicle engine diagnosis often involves multiple signal analysis. The developed system first partitions a leading signal into small segments representing physical events or stateds based on wavelet mutli-resolution analysis. Second, by applying the segmentation result of the leading signal to the other signals, the detailed properties of each segment, including inter-signal relationships, are extracted to form a feature vector. Finally a fuzzy intelligent system is used to learn diagnostic features from a training set containing feature vectors extracted from signal segments at various vehicle states. The fuzzy system applies its diagnostic knowledge to classify signals as abnormal or normal. The implementation of the system is described and experiment results are presented.

Analysis of heart rate variability (HRV) is a valuable, non-invasive method for quantifying autonomic cardiac control in humans. Frequency-domain analysis of HRV involving myocardial ischaemic episodes should take into account its non-stationary behaviour. The wavelet transform is an alternative tool for the analysis of non-stationary signals. Fourteen patients have been analysed, ranging from 40 to 64 years old and selected from the European Electrocardiographic ST-T Database (ESDB).

Time-frequency distribution methods are being widely used for the analysis of a variety of biomedical signals. Recently, they have been applied also to study otoacoustic emissions (OAE's), the active acoustic response of the hearing end organ. Click-evoked otoacoustic emissions (CEOAE's) are time-varying signals with a clear frequency dispersion along with the time axis. Analysis of CEOAE's is of considerable interest due to their close relation with cochlear mechanisms. In this paper, several basic time-frequency distribution methods are considered and compared on the basis of both simulated signals and real CEOAE's. The particular structure of CEOAE's requires a method with both a satisfactory time and frequency resolution. Results from simulations and real CEOAE's revealed that the wavelet approach is highly suitable for the analysis of such signals. Some examples of the application of the wavelet transform to CEOAE's are provided here. Applications range from the extraction of normative data from adult and neonatal OAE's to the extraction of quantitative parameters for clinical purposes.

Pulmonary embolism is an avoidable cause of death if treated immediately but delays in diagnosis and treatment lead to an increased risk. Computer-assisted image analysis of both unenhanced and contrast-enhanced computed tomography (CT) have proven useful for diagnosis of pulmonary embolism. Dual energy CT provides additional information over the standard single energy scan by generating fourdimensional (4D) data, in our case with 11 energy levels in 3D. In this paper a 4D texture analysis method capable of detecting pulmonary embolism in dual energy CT is presented. The method uses wavelet-based visual words together with an automatic geodesic-based region of interest detection algorithm to characterize the texture properties of each lung lobe. Results show an increase in performance with respect to the single energy CT analysis, as well as an accuracy gain compared to preliminary work on a small dataset.

This paper presents method of deriving optimal excitation signal maximizing probability of successful fault diagnosis. The approach uses evolutionary algorithm and wavelet analysis. The diagnosis procedure is conducted by means of specialized aperiodic excitation. Results are compared with fault diagnosis using unit step excitation. The method belongs to simulation before test (SBT) class of fault diagnosis procedure and focuses on case where only input and output nodes of integrated circuit under test (CUT) are available.

We develop a new filter which combines spatially adaptive noise filtering in the wavelet domain and temporal filtering in the signal domain. For spatial filtering, we propose a new wavelet shrinkage method, which estimates how probable it is that a wavelet coefficient represents a "signal of interest" given its value, given the locally averaged coefficient magnitude and given the global subband statistics. The temporal filter combines a motion detector and recursive time-averaging. The results show that this combination outperforms single resolution spatio-temporal filters in terms of quantitative performance measures as well as in terms of visual quality. Even though our current implementation of the new filter does not allow real-time processing, we believe that its optimized software implementation could be used for real-or near real-time filtering.

The characterization of the prominent features of near-fault pulse-like ground motions is under scrutiny. Relationships between pulse characteristics and the performance of structures are here established. Two wavelet energy-based signal processing procedures are introduced. The aim is the construction of simplified signals containing the prominent features of the data distribution recorded from pulse-like earthquakes; signals that can be efficiently used in the design of civil engineering structures, increasing the safety and reliability of the structural design itself. The first procedure is based on the analysis of the absolute input energy. The second one considers the relative input energy. Comparisons with other wavelet-based earthquake analyses are developed.

is applied to the analysis of the nucleotide sequence of the rhodopsin gene of Chinese Hamster cells. The Lipschitz-Hclder exponents for the probability measurements of adenine, guanine, thymine and cytosine distributions are obtained. The local scaling found by means of wavelet analysis is argued to be an indication of long-range correlations.

Objective: We characterised the spectral response of the EEG to median nerve stimulation using wavelet analysis, and compared the relative magnitudes of effect of several different action -observation conditions on the beta and mu 'rebound' rhythms.

Extracting clean fetal electrocardiogram (ECG) signals is very important in fetal monitoring. In this paper, we proposed a new method for fetal ECG extraction based on wavelet analysis, the least mean square (LMS) adaptive filtering algorithm, and the spatially selective noise filtration (SSNF) algorithm. First, abdominal signals and thoracic signals were processed by stationary wavelet transform (SWT), and the wavelet coefficients at each scale were obtained. For each scale, the detail coefficients were processed by the LMS algorithm. The coefficient of the abdominal signal was taken as the original input of the LMS adaptive filtering system, and the coefficient of the thoracic signal as the reference input. Then, correlations of the processed wavelet coefficients were computed. The threshold was set and noise components were removed with the SSNF algorithm. Finally, the processed wavelet coefficients were reconstructed by inverse SWT to obtain fetal ECG. Twenty cases of simulated data and 12 cases of clinical data were used. Experimental results showed that the proposed method outperforms the LMS algorithm:

The use of two dimensional (2-D) continuous wavelet analysis has not been extensive for image processing using wavelets. It has been overshadowed by the 2-D discrete dyadic wavelet transform (DWT) due to its compactness and excellent performance in coding, data compression, image reconstruction, etc. However, the 2-D DWT has some restrictions on the scale and position parameters, and it does not detect all the features of an image unless properly tuned. The 2-D continuous wavelet transform (CWT), on the other hand, is more flexible and provides complete control over the scale and position parameters; and thus it is capable of extracting various features of an image, which cannot be accomplished by the DWT.

Deception is commonly seen in everyday social interactions. However, most of the knowledge about the underlying neural mechanism of deception comes from studies where participants were instructed when and how to lie. To study spontaneous deception, we designed a guessing game modeled after Greene and Paxton (2009) ''Proceedings of the National Academy of Sciences, 106(30), 12506-12511'', in which lying is the only way to achieve the performance level needed to end the game. We recorded neural responses during the game using near-infrared spectroscopy (NIRS). We found that when compared to truth-telling, spontaneous deception, like instructed deception, engenders greater involvement of such prefrontal regions as the left superior frontal gyrus. We also found that the correct-truth trials produced greater neural activities in the left middle frontal gyrus and right superior frontal gyrus than the incorrect-truth trials, suggesting the involvement of the reward system. Furthermore, the present study confirmed the feasibility of using NIRS to study spontaneous deception.

A new method is presented for the purpose of improving pass/fail separation during transient evoked otoacoustic emission (TEOAE) hearing screening. The method combines signal decomposition in scales using the discrete wavelet transform, non-linear denoising and scale-dependent time windowing. The crosscorrelation coefficient between two subaveraged, processed TEOAE signals is used as a pass/fail criterion and assessed in relation to the pure-tone, mean hearing level The performance is presented in terms of receiver operating characteristics for a database of 5214 individuals. The results show that the specificity improves from 68% to 83% at a sensitivity of 90% when compared with the conventional wave reproducibility parameter.

Vibration signals are considered as nonstationary signals with transients. Conventional harmonic Fourier analysis ®nds it dif®cult to model the vibration signals. In this paper, a novel approach using the global Fourier transforms and local wavelet analysis is presented for vibration analysis and modelling. Time±frequency wavelet analysis has been proven a useful tool for the detection of vibration transients. However, current algorithms with discrete or continuous wavelet transforms for vibration analysis are either low resolution of features or very time consuming. We developed a fast Gaussian wavelet algorithm with very narrow band-pass ®ltering technique. The time±frequency maps with high frequency resolution enable us to observe the evolution in time of signi®cant frequencies identi®ed by global Fourier analysis, so that the transients and the regular signals can be distinguished. These regular signi®cant frequencies are selected to be the basis of vibration modelling. The coef®cients of the model are identi®ed by a least-squares algorithm, which ensures that the error is minimised. To demonstrate this approach a machine spindle vibration signal is analysed, and the main features of the vibration signal are extracted, which are useful for system monitoring and further analysis.

A new algorithm for medical image retrieval is presented in the paper. An 8-bit grayscale image is divided into eight binary bit-planes, and then binary wavelet transform (BWT) which is similar to the lifting scheme in real wavelet transform (RWT) is performed on each bitplane to extract the multi-resolution binary images. The local binary pattern (LBP) features are extracted from the resultant BWT sub-bands. Three experiments have been carried out for proving the effectiveness of the proposed algorithm. Out of which two are meant for medical image retrieval and one for face retrieval. It is further mentioned that the database considered for three experiments are OASIS magnetic resonance imaging (MRI) database, NEMA computer tomography (CT) database and PolyU-NIRFD face database. The results after investigation shows a significant improvement in terms of their evaluation measures as compared to LBP and LBP with Gabor transform.

Cancer classification by doctors and radiologists was based on morphological and clinical features and had limited diagnostic ability in olden days. The recent arrival of DNA microarray technology has led to the concurrent monitoring of thousands of gene expressions in a single chip which stimulates the progress in cancer classification. In this paper, we have proposed a hybrid approach for microarray data classification based on nearest neighbor (KNN), naive Bayes, and support vector machine (SVM). Feature selection prior to classification plays a vital role and a feature selection technique which combines discrete wavelet transform (DWT) and moving window technique (MWT) is used. The performance of the proposed method is compared with the conventional classifiers like support vector machine, nearest neighbor, and naive Bayes. Experiments have been conducted on both real and benchmark datasets and the results indicate that the ensemble approach produces higher classification accura...

Recent studies provide evidence for the multi-scale nature of magnetic turbulence in the plasma sheet. Wavelet methods represent modern time series analysis techniques suitable for the description of statistical characteristics of multi-scale turbulence. Cluster FGM (fluxgate magnetometer) magnetic field high-resolution (67 Hz) measurements are studied during an interval in which the spacecraft are in the plasma sheet. As Cluster passes through different plasma regions, physical processes exhibit non-steady properties on magnetohydrodynamic (MHD) and small, possibly kinetic scales. As a consequence, the implementation of wavelet-based techniques becomes complicated due to the statistically transitory properties of magnetic fluctuations and finite size effects. Using a supervised multi-scale technique which allows existence test of moments, the robustness of higher-order statistics is investigated. On this basis the properties of magnetic turbulence are investigated for changing thickness of the plasma sheet.

Using recent advances in time-varying spectral methods, this research analyses the growth cycles of productivity for three economies: that of the euro area, the US and the UK. The methodology uses a discrete wavelet transform (MODWT), a continuous wavelet transform (CWT) and also Hilbert wavelet pairs in order to analyze bivariate time series in terms of conventional frequency domain measures from spectral analysis. The …ndings are that there appears to be cycles at various frequencies, apart from the usual longer cycle that the economics literature focuses on, and there is apparently little signi…cant correlation or coherence between productivity cycles between the three, signifying that country-idiosyncratic factors are much more likely to drive productivity than international factors.

Temperature reconstructions from Europe for the past 500 years based on documentary and instrumental data are analysed. First, the basic documentary data sources, including information about climate and weather-related extremes, are described. Then, the standard palaeoclimatological reconstruction method adopted here is discussed with a particular application to temperature reconstructions from documentary-based proxy data. The focus is on two new reconstructions; January–April mean temperatures for Stockholm (1502–2008), based on a combination of data for the sailing season in the Stockholm harbour and instrumental temperature measurements, and monthly Central European temperature (CEuT) series (1500–2007) based on documentary-derived temperature indices of the Czech Republic, Germany and Switzerland combined with instrumental records from the same countries. The two series, both of which are individually discussed in greater detail in subsequent papers in this special edition, are here compared and analysed using running correlations and wavelet analysis. While the Stockholm series shows a pronounced low-frequency component, the CEuT series indicates much weaker low-frequency variations. Both series are analysed with respect to three different long-period reconstructions of the North Atlantic Oscillation (NAO) and are compared with other European temperature reconstructions based on tree-rings, wine-harvest data and various climate multiproxies. Correlation coefficients between individual proxy-based series show weaker correlations compared to the instrumental data. There are also indications of temporally varying temperature cross-correlations between different areas of Europe. The two temperature reconstructions have also been compared to geographically corresponding temperature output from simulations with global and regional climate models for the past few centuries. The findings are twofold: on the one hand, the analysis reinforces the hypothesis that the index-data based CEuT reconstruction may not appropriately reflect the centennial scale variations. On the other hand, it is possible that climate models may underestimate regional decadal variability. By way of a conclusion, the results are discussed from a broader point of view and attention is drawn to some new challenges for future investigations in the historical climatology in Europe.

In this paper, we propose to extract the texture features of currency note images. To extract the features, first the Discrete Wavelet Transform (DWT) in particular Daubechies 1 (DB1) is utilized on a currency note and the approximate coefficient matrix of the transformed image is obtained. A set of coefficient statistical moments are then extracted from the approximate efficient matrix. The extracted features are stored in a feature vector. The extracted features can be used for recognition, classification and retrieval of currency notes.

Gradual development of anomalies (i.e., deviations from the nominal condition) may alter the quasi-static behavior patterns of human-engineered complex systems. This chapter presents a recently reported technique of pattern recognition, called Symbolic Dynamic Filtering (SDF), for early detection and prognosis of such changes in behavior patterns due to slowly evolving anomalies that may be benign or malignant. The underlying concept of SDF is built upon the principles of Symbolic Dynamics, Information Theory, and Statistical Signal Processing, where time series data from selected sensor(s) in the fast time scale of the process dynamics are analyzed at discrete epochs in the slow time scale of anomaly evolution. The key idea here is early detection and identification of (possible) changes in quasi-static statistical patterns of the dynamical system behavior. An important feature of this pattern recognition technique is extraction of the relevant statistics by conversion of the time series data into a symbol sequence by appropriate coarse-graining of the imbedded information. As an alternative to the currently practiced method of phase-space partitioning in the time domain, a new concept of partitioning is introduced for symbol generation, based on wavelet analysis of the time series data. This chapter also discusses various aspects of the wavelet-based partitioning tool, such as selection of the wavelet basis, noise mitigation, and robustness to spurious disturbances. The partitioning scheme is built upon the principle of maximum entropy such that the regions of the data space with more information are partitioned finer and those with sparse information are partitioned coarser. The algorithms of SDF are constructed to solve two problems: (i) Forward problem of Pattern Recognition for (offline) characterization of the anomalous behavior, relative to the nominal behavior; and (ii) Inverse problem of Pattern * Identification for (online) estimation of parametric or non-parametric changes based on the knowledge assimilated in the forward problem and the observed time series data of quasi-stationary process response.

Analysis of heart rate variation (HRV) has become a popular non-invasive tool for assessing the activities of the autonomic nervous system (ANS). HRV analysis is based on the concept that fast fluctuations may specifically reflect changes of sympathetic and vagal activity. It shows that the structure generating the signal is not simply linear, but also involves nonlinear contributions. These signals are essentially nonstationary; may contain indicators of current disease, or even warnings about impending diseases. The indicators may be present at all times or may occur at random in the time scale. However, to study and pinpoint abnormalities in voluminous data collected over several hours is strenuous and time consuming. This paper presents the continuous time wavelet analysis of heart rate variability signal for disease identification. Fractal dimension (FD) of heart rate signals are calculated and compared with the wavelet analysis patterns. The FD obtained indicates more than 90% confidence interval for all the classes studied.

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.

In this paper, we investigate the price spillover effects among two developed markets, (the US and the UK), and two developing markets, (Irish and Portuguese), using a new testing method suggested by Lee (2002). We find that there are interrelationships between any two of the Irish, the UK and Portuguese markets and that the co-movements between the emerging markets and the US are statistically significant but weak. We also found that the US market is slightly influenced by the UK but not vice versa.

In this paper, we investigate the price interdependence between seven international stock markets, namely Irish, UK, Portuguese, US, Brazilian, Japanese and Hong Kong, using a new testing method, based on the wavelet transform to reconstruct the data series, as suggested by Lee [11]. We find evidence of intra-European (Irish, UK and Portuguese) market co-movements with the US market also weakly influencing the Irish market. We also find co-movement between the US and Brazilian markets and similar intra-Asian co-movements (Japanese and Hong Kong). Finally, we conclude that the circle of impact is that of the European markets (Irish, UK and Portuguese) on both American markets (US and Brazilian), with these in turn impacting on the Asian markets (Japanese and Hong Kong) which in turn influence the European markets. In summary, we find evidence for intra-continental relationships and an increase in importance of international spillover effects since the mid 1990s, while the importance ...

Several studies have reported the asynchronous closure of normal bileaflet valves (NBVs), resulting in a split in its closing sound; however, the clinical significance of this split has never been studied in malfunctioning bileaflet valves (MBVs). The study comprised 218 valves in 184 patients, including normal monoleaflet valves (n = 10), NBVs (n = 198), and MBVs (n = 10). Valve function was confirmed by cinefluoroscopy prior to analysis of the valve sound by the Morlet continuous wavelet transform (CWT). The split interval (SI) for each heartbeat was measured, and the coefficient of variation (CV) of its mean (valve SI) was calculated as a parameter for the fluctuation of the SI. The CWT of monoleaflet valves showed a single spike, whereas NBVs exhibited a clear split. There was no significant difference in valve SI between the aortic and mitral positions; however, the mean of the CV was significantly greater in the mitral position (n = 90, 0.507 +/- 0.254) than in aortic position...

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 ] (]]]]) ]]]-]]]

Fatigue in rolling element bearings, resulting in spalling of the races and/or rolling elements, is the most common cause of bearing failure. The useful life of the bearing may extend considerably beyond the appearance of the first spall and a premature removal of the bearing from service can be very expensive, but on the other hand chances cannot be taken with safety of machines or personnel. Previous studies indicated that there might be two parts to the defect vibration signal of a spalled bearing, the first part being originating from the entry of the rolling element into the fault (de-stress) and the second part being due to the departure of the rolling element from the fault (re-stress). This is investigated in this paper using vibration signatures of seeded faults at different speeds. The acceleration signals resulting from the entry of the rolling element into the spall and exit from it were found to be of different natures. The entry into the fault can be described as a step response, with mainly low frequency content, while the impact excites a much broader frequency impulse response. The latter is the most noticeable and prominent event, especially when examining the high pass filtered response or the enveloped signal. In order to enable a clear separation of the two events, and produce an averaged estimate of the size of the fault, two approaches are proposed to enhance the entry event while keeping the impulse response. The first approach (joint treatment) utilizes pre-whitening to balance the low and high frequency energy, then octave band wavelet analysis to allow selection of the best band (or scale) to balance the two pulses with similar frequency content. In the second approach, a separate treatment is applied to the step and the impulse responses, so that they can be equally represented in the signal. Cepstrum analysis can be used to give an average estimate of the spacing between the entry and impact events, but the latter can also be assessed by an arithmetic estimation of the mean and standard deviation of the event separation for a number of realizations, in particular for the second approach. In order to determine the effects of various simulations and signal processing parameters on the estimated delay times, the entry and exit events were simulated as modified step and impulse responses with precisely known starting times. The simulation was also found useful in pointing to artefacts associated with the cepstrum calculation, which affect even the simulated signals, and have thus prompted modifications of the processing of real signals. The results presented for the two approaches give a reasonable approximation of the measured fault widths (double the spacing between the entry and impact events) under different speed conditions, but the method of separate treatment is somewhat better and is thus recommended.

Alternative or complementary medicine emphasizes therapies that are claimed to improve quality of life, prevent disease, and address conditions that conventional medicine has limited success in curing. There are many techniques which are prevalent in many countries and these can cause harm if not scientifically evaluated. The objective of this paper is to validate the use of iridology to diagnose kidney abnormalities. Two subject groups were evaluated: one was 168 subjects free from kidney disease and the other was 172 subjects with chronic renal failure. The procedure to acquire, process and classify the iris images was designed in such a way that avoids any dependency on the iridologists by using wavelet analysis and Adaptive Neuro-Fuzzy Inference System. The results show a correct classification for both subjects with kidney problems and normal subjects of 82% and 93%, respectively. The proposed technique conducted on a systemic disease with ocular manifestations showed encouraging results. However, it is necessary to perform extensive studies with diseases that do not have ocular manifestations according to conventional medicine in order to validate iridology as a valid scientific technique.

We propose a form of semi-nonparametric regression based on wavelet analysis. Traditional time series methods usually involve either the time or the frequency domain, but wavelets can combine the information from both of these. While wavelet transforms are typically restricted to equally spaced observations an integer power of 2 in number, we show how to go beyond these constraints. We use our methods to construct \patios" for 21 important international commodity price series. These graph the magnitude of the variations in the series at di erent time scales for various subperiods of the full sample.

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.

In this paper, we investigate the price spillover effects among two developed markets, (the US and the UK), and two developing markets, (Irish and Portuguese), using a new testing method suggested by Lee (2002). We find that there are interrelationships between any two of the Irish, the UK and Portuguese markets and that the co-movements between the emerging markets and the US are statistically significant but weak. We also found that the US market is slightly influenced by the UK but not vice versa.

Identifying spatio-temporal synchrony in a complex, interacting and oscillatory coupled-system is a challenge. In particular, the characterization of statistical relationships between environmental or biophysical variables with the multivariate data of pandemic is a difficult process because of the intrinsic variability and non-stationary nature of the time-series in space and time. This paper presents a methodology to address these issues by examining the bivariate relationship between Covid-19 and temperature time-series in the time-localized frequency domain by using Singular Value Decomposition (SVD) and continuous cross-wavelet analysis. First, the dominant spatio-temporal trends are derived by using the eigen decomposition of SVD. The Covid-19 incidence data and the temperature data of the corresponding period are transformed into significant eigen-state vectors for each spatial unit. The Morlet Wavelet transformation is performed to analyse and compare the frequency structure of the dominant trends derived by the SVD. The result provides cross-wavelet transform and wavelet coherence measures in the ranges of time period for the corresponding spatial units. Additionally, wavelet power spectrum and paired wavelet coherence statistics and phase difference are estimated. The result suggests statistically significant coherency at various frequencies providing insight into spatio-temporal dynamics. Moreover, it provides information about the complex conjugate dynamic relationships in terms phases and phase differences.

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. #

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Seasonal and annual rainfall data of the stations: Akluj, Baramati, Bhor and Malsiras stations located in Nira Basin, Central India, were analyzed for studying trend and periodicity using 104 years’ rainfall data. The analysis was carried out by using Mann-Kendall (MK), Modified Mann-Kendall (MMK) and Theil and Sen’s slope estimator tests describing rising trend at all the stations. However, it is statistically significant at Akluj and Bhor stations at 10% significance level. Bhor station showed the maximum increase in percentage change i.e. 0.28% in annual rainfall. Monsoon and post-monsoon seasonal rainfall shows a rising trend while the summer and winter seasonal rainfall shows a falling trend. Wavelet analysis showed prominent annual rainfall periods ranging from 2 to 8 years at all the stations after 1960s resulting in describing more changes in the rainfall patterns after 1960s.

A model for a financial asset is constructed with two types of agents, who differ in terms of their beliefs. The proportion of the two types changes over time according to stochastic processes which model the interaction between the agents. Agents do not persist in holding "wrong" beliefs and bubble-like phenomena in the asset price occur. We consider tests for detecting bubbles in the conditional mean and multiple changes in the conditional variance of the process. A wavelet analysis of the series generated by our models shows that the strong persistence in the volatility is likely to be the outcome of a mix of changes in regimes and a moderate level of long-range dependence. These results are consistent with what has been observed by and .

The Sun is the nearest stellar and astrophysical laboratory, available for detailed studies in several fields of physics and astronomy. It is a sphere of hot gas with a complex and highly variable magnetic field which plays a very important role. The Sun shows an unprecedented wealth of phenomena that can be studied extensively and to the greatest detail, in a way we will never be in a position to study in other stars. Humans have studied the Sun for millennia and after the discovery of the telescope they realized that the Sun varies with time, i.e., solar activity is highly variable, in tune scales of millennia to seconds. The study of these variabilities helps us to understand how the Sun works and how it affects the interplanetary medium, Earth and the other planets. Solar power varies substantially and greatly affects the Earth and humans. Solar activity has several important periodicities, and quasi-periodicities. Knowledge of these periodicities helps us to forecast, to an extent, solar events that affect our planet. The most prominent periodicity of solar activity is the one of 11 years. The actual period is in fact 22 years because the magnetic field polarity of the Sun has to be taken into account. The Sun can be considered as a non-linear RLC electric circuit with a period of 22 years. The RLC equivalent circuit of the Sun is a van der Pol oscillator and such a model can explain many solar phenomena, including the variability of solar energy with time. Other quasi-periodicities such as the ones of 154 days, the 1.3, 1.7 to 2 years, etc., some of which might be harmonics of the 22 year cycle are also present in solar activity, and their study is very interesting and important since they affect the Earth and human activities. The period of 27 days related to solar rotation plays also a very important role in geophysical phenomena. It is noticeable that almost all periodicities are highly variable with time as wavelet analysis reveals. It is very important for humans to be in a position to forecast solar activity during the next hour, day, year, decade and century, because solar phenomena affect life on Earth and such predictions will help politicians and policy makers to better serve their countries and our planet. (X. Moussas). z Deceased. 1 We can assume astronomers are the only humans that their life is affected by the stars since they make their living with them, although people believing in astrology are also affected by the stars. www.elsevier.com/locate/asr Advances in Space Research 35 (2005) 725-738

In this paper, we investigate the price interdependence between seven international stock markets, namely Irish, UK, Portuguese, US, Brazilian, Japanese and Hong Kong, using a new testing method, based on the wavelet transform to reconstruct the data series, as suggested by Lee (2002). We find evidence of intra-European (Irish, UK and Portuguese) market co-movements with the US market also weakly influencing the Irish market. We also find co-movement between the US and Brazilian markets and similar intra-Asian co-movements (Japanese and Hong Kong). Finally, we conclude that the circle of impact is that of the European markets (Irish, UK and Portuguese) on both American markets (US and Brazilian), with these in turn impacting on the Asian markets (Japanese and Hong Kong) which in turn influence the European markets. In summary, we find evidence for intra-continental relationships and an increase in importance of international spillover effects since the mid 1990’s, while the importan...