Cross-wavelet Spectra Research Articles

Seasonal Influenza Epidemics and El Niños.

Seasonal influenza epidemics occur annually during the winter in the northern and southern hemispheres, but timing of peaks and severity vary seasonally. Low humidity, which enhances survival and transmission of influenza virus, is the major risk factor. Both El Niño and La Niña phases of El Niño-southern oscillation (ENSO), which determine inter-annual variation of precipitation, are putative risk factors. This study was done to determine if seasonality, timing of peak, and severity of influenza epidemics are coupled to phases of ENSO. Monthly time series of positive specimens for influenza viruses and of multivariate El Niño-Southern Oscillation Index from January 2000 to August 2015 were analyzed. Seasonality, wavelet spectra, and cross-wavelet spectra analyses were performed. Of 31 countries in the dataset, 21 were in the northern hemisphere and 10 in the southern hemisphere. The highest number of influenza cases occurred in January in the northern hemisphere, but in July in the southern hemisphere, p < 0.0001. Seasonal influenza epidemic was coupled to El Niño, while low occurrence was coupled to La Niña. The moderate La Niña of 2010–2011 was followed by weak seasonal influenza epidemic. The influenza pandemic of 2009–2010 followed the moderate El Niño of 2009–2010, which had three peaks. Spectrograms showed time-varying periodicities of 6–48 months for ENSO, 6–24 months for influenza in the northern hemisphere, and 6–12 months for influenza in the southern hemisphere. Cross spectrograms showed time-varying periodicities at 6–36 months for ENSO and influenza in both hemispheres, p < 0.0001. Phase plots showed that influenza time series lagged ENSO in both hemispheres. Severity of seasonal influenza increases during El Niño, but decreases during La Niña. Coupling of seasonality, timing, and severity of influenza epidemics to the strength and waveform of ENSO indicate that forecast models of El Niño should be integrated into surveillance programs for influenza epidemics.

A new method to calculate the time delay of the Pi2 pulsations

The time delay determination of the Pi2 pulsations could provide more understanding of the propagation characteristics of the Pi2. Few studies have concerned with the time delay of Pi2 pulsation. We present a new method to calculate the time delay of Pi2 pulsations using cross wavelet technique. We study 48 events occurred in March 2008 and February–May 2009 at Carson City (CCNV), McGrath (MCGR), The Pas (TPAS) and Kuujjuarapik (KUUJ) stations which belong to the ground magnetometer network of the Time History of Events and Macroscale Interactions during Substorms (THEMIS). The cross wavelet spectrum showed a comparable time with that obtained using cross correlation method. We suggest that the cross wavelet technique can be effectively used to calculate the time delay of Pi2 pulsation and further used as a substitute for cross correlation method.

Long-term response of stratospheric ozone and temperature to solar variability

Abstract. The long-term variability in stratospheric ozone mass mixing ratio (O3) and temperature (T) from 1979 to 2013 is investigated using the latest reanalysis product delivered by the European Centre for Medium-Range Weather Forecasts (ECMWF), i.e., ERA-Interim. Moreover, using the Mg II index time series for the same time period, the response of the stratosphere to the 11-year Schwabe solar cycle is investigated. Results reveal the following features: (i) upward (downward) trends characterize zonally averaged O3 anomalies in the upper (middle to lower stratosphere) stratosphere, while prevailing downward trends affect the T field. Mg II index data exhibit a weaker 24th solar cycle (though not complete) when compared with the previous two; (ii) correlations between O3 and Mg II, T and Mg II, and O3 and T are consistent with photochemical reactions occurring in the stratosphere and large-scale transport; and (iii) wavelet cross-spectra between O3 and Mg II index show common power for the 11-year period, particularly in tropical regions around 30–50 hPa, and different relative phase in the upper and lower stratosphere. A comprehensive insight into the actual processes accounting for the observed correlation between ozone and solar UV variability would be gained from an improved bias correction of ozone measurements provided by different satellite instruments, and from the observations of the time behavior of the solar spectral irradiance.

A Cross-Wavelet Transform Aided Rule Based Approach for Early Prediction of Lean Blow-out in Swirl-Stabilized Dump Combustor

Lean or ultralean combustion is one of the popular strategies to achieve very low emission levels. However, it is extremely susceptible to lean blow-out (LBO). The present work explores a Cross-wavelet transform (XWT) aided rule based scheme for early prediction of lean blowout. XWT can be considered as an advancement of wavelet analysis which gives correlation between two waveforms in time-frequency space. In the present scheme a swirl-stabilized dump combustor is used as a laboratory-scale model of a generic gas turbine combustor with LPG as fuel. Various time series data of CH chemiluminescence signal are recorded for different flame conditions by varying equivalence ratio, flow rate and level of air-fuel premixing. Some features are extracted from the cross-wavelet spectrum of the recorded waveforms and a reference wave. The extracted features are observed to classify the flame condition into three major classes: near LBO, moderate and healthy. Moreover, a Rough Set based technique is also applied on the extracted features to generate a rule base so that it can be fed to a real time controller or expert system to take necessary control action to prevent LBO. Results show that the proposed methodology performs with an acceptable degree of accuracy.

Pc5 Magnetic Pulsations during the Outer Electron Radiation Belt

Since the discovery of the radiation belt decades ago, there still remain some fundamental questions as to which one is the mechanism responsible for the acceleration of electrons. Groundbased Pc5 magnetic pulsation during the process of increasing of 2-MeV electron fluxes has been analyzed. First, a filter bandpass in the period range of 150-600 seconds has been used to localize the Pc5 waves. Second, we then applied a wavelet transform procedure, whereby the Morlet function as a mother wavelet was selected to analyze Pc5 wave packets. First, we show that dynamic pressure of solar wind controls the power of Pc5 magnetic pulsations. Second, by performing a cross-spectrum analysis of Pc5 wavelet during electron radiation belts we show that the wavelet power of Pc5 magnetic pulsations which is associated with a maximum wavelet cross spectrum show a similar change of Pc5 pulsations occurs during radiation belt events. Increasing of electron fluxes which is initiated by the presence of large power of Pc5 magnetic pulsations has been observed. This indicates that Pc5 magnetic pulsations could play a role in the acceleration and transport mechanism of the electron radiation belt. Also, 4-5 days from the beginning of increasing of electron fluxes we observed globally, a depression in the power of Pc5 magnetic pulsations as well as a monotonically decreasing of the solar wind dynamic pressure. On the other hand, during the end period of the electron belt, we also observed a sudden increasing of Pc5 power. We suggest that during the expansion periode of the outer electron radiation belt outward to interplanetary electron belt pressure that will reduce the solar wind dynamic pressure and consequently a decrease occurs in the power of Pc5 magnetic pulsation. And, in the end period of the electron radiation belt the electron fluxes back to its normal level and consequently a sudden increase of the Pc5 solar wind dynamic pressure occurs and that sudden increase also drives the sudden increasing power of Pc5 magnetic pulsations.

Thalamomuscular coherence in essential tremor: hen or egg in the emergence of tremor?

Thalamomuscular coherence in essential tremor (ET) has consistently been detected in numerous neurophysiological studies. Thereby, spatial properties of coherence indicate a differentiated, somatotopic organization; so far, however, little attention has been paid to temporal aspects of this interdependency. Further insight into the relationship between tremor onset and the onset of coherence could pave the way to more efficient deep brain stimulation (DBS) algorithms for tremor. We studied 10 severely affected ET patients (six females, four males) during surgery for DBS-electrode implantation and simultaneously recorded local field potentials (LFPs) and surface electromyographic signals (EMGs) from the extensor and flexor muscles of the contralateral forearm during its elevation. The temporal relationship between the onset of significant wavelet cross spectrum (WCS) and tremor onset was determined. Moreover, we examined the influence of electrode location within one recording depth on this latency and the coincidence of coherence and tremor for depths with strong overall coherence ("tremor clusters") and those without. Data analysis revealed tremor onset occurring 220 ± 460 ms before the start of significant LFP-EMG coherence. Furthermore, we could detect an anterolateral gradient of WCS onset within one recording depth. Finally, the coincidence of tremor and coherence was significantly higher in tremor clusters. We conclude that tremor onset precedes the beginning of coherence. Besides, within one recording depth there is a spread of the tremor signal. This reflects the importance of somatosensory feedback for ET and questions the suitability of thalamomuscular coherence as a biomarker for "closed-loop" DBS systems to prevent tremor emergence.

Climatic-driven seasonality of emerging dengue fever in Hanoi, Vietnam.

BackgroundDengue fever (DF) has been emerging in Hanoi over the last decade. Both DF epidemiology and climate in Hanoi are strongly seasonal. This study aims at characterizing the seasonality of DF in Hanoi and its links to climatic variables as DF incidence increases from year to year.MethodsClinical suspected cases of DF from the 14 central districts of Hanoi were obtained from the Ministry of Health over a 8-year period (2002–2009). Wavelet decompositions were used to characterize the main periodic cycles of DF and climatic variables as well as the mean phase angles of these cycles. Cross-wavelet spectra between DF and each climatic variables were also computed. DF reproductive ratio was calculated from Soper’s formula and smoothed to highlight both its long-term trend and seasonality.ResultsTemperature, rainfall, and vapor pressure show strong seasonality. DF and relative humidity show both strong seasonality and a sub-annual periodicity. DF reproductive ratio is increasing through time and displays two clear peaks per year, reflecting the sub-annual periodicity of DF incidence. Temperature, rainfall and vapor pressure lead DF incidence by a lag of 8–10 weeks, constant through time. Relative humidity leads DF by a constant lag of 18 weeks for the annual cycle and a lag decreasing from 14 to 5 weeks for the sub-annual cycle.ConclusionResults are interpreted in terms of mosquito population dynamics and immunological interactions between the different dengue serotypes in the human compartment. Given its important population size, its strong seasonality and its dengue emergence, Hanoi offers an ideal natural experiment to test hypotheses on dengue serotypes interactions, knowledge of prime importance for vaccine development.

Long term variability of the Danube River flow and its relation to precipitation and air temperature

In this work the long cycles and long range dependence of monthly discharge, precipitation and air temperature time series from the Danube River during the years 1901–2006 were analysed using wavelet analysis, with emphasis on wavelet coherence and cross wavelet spectra. All time series were deseasonalized prior to the analysis. Long cycles with 11–15 year periods during almost the whole observed period in discharge and during 1935–1975 in precipitation were found. Furthermore a reappearing four year cycle was found in all discharge time series. No significant long cycles were found in the temperature time series, which on the other hand display long term persistence. The cross-wavelet spectra and the wavelet coherence show strong correlation between the precipitation and discharge spectra in the low frequency intervals. Furthermore, a convolution of precipitation and catchment response function was used to examine the propagation of long cycles from precipitation to discharge. The results show, that the long range dependence in precipitation propagates into discharge and that the precipitation lead in the cross-wavelet spectrum increases with the increasing response time. The results indicate that especially mean monthly precipitation could be used as input variable in order to improve stochastic discharge modelling.

Application of Cross Wavelet Transform for ECG Pattern Analysis and Classification

In this paper, we use cross wavelet transform (XWT) for the analysis and classification of electrocardiogram (ECG) signals. The cross-correlation between two time-domain signals gives a measure of similarity between two waveforms. The application of the continuous wavelet transform to two time series and the cross examination of the two decompositions reveal localized similarities in time and frequency. Application of the XWT to a pair of data yields wavelet cross spectrum (WCS) and wavelet coherence (WCOH). The proposed algorithm analyzes ECG data utilizing XWT and explores the resulting spectral differences. A pathologically varying pattern from the normal pattern in the QT zone of the inferior leads shows the presence of inferior myocardial infarction. A normal beat ensemble is selected as the absolute normal ECG pattern template, and the coherence between various other normal and abnormal subjects is computed. The WCS and WCOH of various ECG patterns show distinguishing characteristics over two specific regions R1 and R2, where R1 is the QRS complex area and R2 is the T-wave region. The Physikalisch-Technische Bundesanstalt diagnostic ECG database is used for evaluation of the methods. A heuristically determined mathematical formula extracts the parameter(s) from the WCS and WCOH. Empirical tests establish that the parameter(s) are relevant for classification of normal and abnormal cardiac patterns. The overall accuracy, sensitivity, and specificity after combining the three leads are obtained as 97.6%, 97.3%, and 98.8%, respectively.

Geophysical Applications of Partial Wavelet Coherence and Multiple Wavelet Coherence

Abstract In this paper, the application of partial wavelet coherence (PWC) and multiple wavelet coherence (MWC) to geophysics is demonstrated. PWC is a technique similar to partial correlation that helps identify the resulting wavelet coherence (WTC) between two time series after eliminating the influence of their common dependence. MWC, akin to multiple correlation, is, however, useful in seeking the resulting WTC of multiple independent variables on a dependent one. The possible El Niño–Southern Oscillation–related impact of the large-scale atmospheric factors on tropical cyclone activity over the western North Pacific is used as an example. A software package for PWC and MWC has been developed. It also includes modified software that rectified the bias in the wavelet power spectrum and wavelet cross-spectrum. The package is available online (see http://www.cityu.edu.hk/gcacic/wavelet).

Solar-Terrestrial Signal Record in Tree Ring Width Time Series from Brazil

This work investigates the behavior of the sunspot number and Southern Oscillation Index (SOI) signal recorded in the tree ring time series for three different locations in Brazil: Humaita in Amazonia State, Porto Ferreira in Sao Paulo State, and Passo Fundo in Rio Grande do Sul State, using wavelet and cross-wavelet analysis techniques. The wavelet spectra of tree ring time series showed signs of 11 and 22 years, possibly related to the solar activity, and periods of 2–8 years, possibly related to El Nino events. The cross-wavelet spectra for all tree ring time series from Brazil present a significant response to the 11-year solar cycle in the time interval between 1921 to after 1981. These tree ring time series still have a response to the second harmonic of the solar cycle (5.5 years), but in different time intervals. The cross-wavelet maps also showed that the relationship between the SOI x tree ring time series is more intense, for oscillation in the range of 4–8 years.

Hand dominance during constant force isometric contractions: evidence of different cortical drive commands

The purpose of this study was to investigate force variability and sensoriomotor strategies of dominant and nondominant hands of right and left-handed subjects during a submaximal isometric force production task. Twelve right-handed adults (9 men and 3 women; 23±3year) and twelve left-handed adults (4 men and 8 women; 24±3year) performed an isometric constant force contraction sustained at 30 and 50% of maximal force for 10s. Surface EMG signals were obtained from forearm flexors and extensors. Force signals were analyzed in the time (CV of force) and frequency (0-10Hz) domain. The neural activation of the involved muscles was investigated from the EMG structure using the cross-wavelet spectra of the interference EMG signals of six different frequency bands of the EMG signals were quantified (5-13, 13-30, 30-60, 60-100, 100-150 and 150-200Hz). The major findings were: (1) dominant and nondominant hands of right- and left-handed subjects exhibited similar CV of force; (2) the power spectrum of force is influenced by handedness, with greater 1-3Hz oscillations for left-handed subjects when compared to right-handed subjects; (3) right-handed subjects have greater 30-60Hz neuromuscular activation when compared to left-handed subjects. Our results indicate that right-handed individuals may rely preferentially in visual feedback to carry out a task with visual and proprioceptive feedback because of the left hemisphere specialization on the visuomotor control.

Bearing system health condition monitoring using a wavelet cross-spectrum analysis technique

Rolling-element bearings are widely used in rotary machinery systems. Accordingly, a reliable bearing fault detection technique is critically needed in industries to prevent the machinery system's performance degradation, malfunction, or even catastrophic failures. Bearing fault detection, however, still remains a very challenging task because most of the bearing fault related signatures are non-stationary. In this paper, a wavelet cross-spectrum (WCS) technique is proposed to tackle the challenge of feature extraction from these non-stationary signatures for bearing fault detection. The vibration signals are first analyzed by a wavelet transform to demodulate primary representative features; the periodic features are then enhanced by cross-correlating the resulting wavelet coefficient functions over several contributive neighboring wavelet bands. A Jarque-Bera statistic index is suggested for the bandwidth selection. The effectiveness ofthe proposed technique is examined by a series of experimental tests corresponding to different bearing conditions. Test results show that the developed WCS technique is an effective signal processing approach for not only stationary but also non-stationary feature extraction and analysis, and it can be applied effectively for bearing fault detection.

Minimization of Harmonics Noise Using Wavelet Transformation Technology

The field programmable gate array technology can design high performance system at low cost for wavelet analysis. Wavelet transform has gained the reputation of being a very effective signal analysis tool for much practical application. Implementation of transform needs the meeting of real-time processing for most application. The objectives of this paper are to compare the Haar and Daubeches technology and to calculate the bit error rate (BER) between the input audio signal and reconstructed output signal. It is seen that the BER using Daubechies wavelet technology is less than Haar wavelet. The design procedure is explained using the stat of art electronic design. Automation tools for system design on FPGA, simulation, synthesis and implementation on the FPGA technology has been carried out. The power hovmoller, cross wavelet spectra and coherence are described. A Practical step-up-step guide to wavelet analysis is given with examples taken from time series. The guide includes a comparison to the windowed Fourier transform. New statistical significance test for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise. Empirical formula is given for the effect of smoothing on significance levels and filtering. The notion of orthogonal no separable trivet wavelet packets, which is the generation of orthogonal university wavelet packets is introduced. A de-noising method based on wavelet packet shrinkage is developed. The principle of wavelet packet shrinkage for de-noising and the section of thresholds and threshold function are analyzed.

Short-Wave Signatures of Stratospheric Mountain Wave Breaking

Abstract Recent stratospheric mountain wave measurements over the Sierra Nevada indicate that downgoing secondary waves may be common or even ubiquitous in large wave events. Because of their short wavelengths, they may dominate the vertical velocity field near the tropopause, and they give a remote indicator of wave breaking farther aloft. Using a 2D numerical model, the authors have simulated the secondary wave generation process with qualitative agreement in the wave location, phase speed, wavelength (i.e., 10–20 km), and amplitude. A key to the analysis was the use of Morlet wavelet cross spectra on both the observational and simulated fields. Several characteristics of the simulated secondary waves were unexpected. First, the secondary waves are generated with good efficiency, approaching 20% of the primary upgoing wave momentum flux. Second, whereas most of the secondary waves are downward, the shorter components reflect upward from the tropopause, giving a kind of lee wave trapping in the lower stratosphere. Long waves are also observed propagating upward and downward away from the wave breaking region. Third, the phase speed of the secondary waves is nearly zero so the Eliassen–Palm relationship between momentum and energy flux is satisfied. While the 2D results are robust to grid size and subgrid parameterization, an extension of the modeling to three dimensions is disappointing. The secondary waves’ amplitudes in the 3D runs are much smaller than observed.

A new statistical test based on the wavelet cross-spectrum to detect time–frequency dependence between non-stationary signals: Application to the analysis of cortico-muscular interactions

The study of the correlations that may exist between neurophysiological signals is at the heart of modern techniques for data analysis in neuroscience. Wavelet coherence is a popular method to construct a time–frequency map that can be used to analyze the time–frequency correlations between two time series. Coherence is a normalized measure of dependence, for which it is possible to construct confidence intervals, and that is commonly considered as being more interpretable than the wavelet cross-spectrum (WCS). In this paper, we provide empirical and theoretical arguments to show that a significant level of wavelet coherence does not necessarily correspond to a significant level of dependence between random signals, especially when the number of trials is small. In such cases, we demonstrate that the WCS is a much better measure of statistical dependence, and a new statistical test to detect significant values of the cross-spectrum is proposed. This test clearly outperforms the limitations of coherence analysis while still allowing a consistent estimation of the time–frequency correlations between two non-stationary stochastic processes. Simulated data are used to investigate the advantages of this new approach over coherence analysis. The method is also applied to experimental data sets to analyze the time–frequency correlations that may exist between electroencephalogram (EEG) and surface electromyogram (EMG).

Energy Flux and Wavelet Diagnostics of Secondary Mountain Waves

Abstract In recent years, aircraft data from mountain waves have been primarily analyzed using velocity and temperature power spectrum and momentum flux estimation. Herein it is argued that energy flux wavelets (i.e., pressure–velocity wavelet cross-spectra) provide a more powerful tool for locating and classifying different types of mountain waves. In the first part of the paper, pressure–velocity cross-spectra using various linear mountain-wave solutions are shown to be capable of disentangling collocated waves with different propagation directions and wavelength. A field of group velocity vectors can also be determined. In the second part, the energy flux wavelet technique is applied to five cases of mountain waves entering the stratosphere from the Terrain-Induced Rotor Experiment (T-REX) in 2006. Perturbation pressure along the flight track is determined using aircraft static pressure corrected hydrostatically with GPS altitude. In four of the cases, collocated long up-propagating and short down-propagating waves are seen in the stratosphere. These waves have strong, but opposite, p′w′ cospectra. In one of these cases, a patch of turbulence is collocated with the up and down waves. In two other cases, trapped waves riding on the tropopause inversion layer (TIL) are seen. These trapped waves have p′w′ quadrature spectra that reverse sign across the tropopause. These newly discovered wave types may arise from secondary wave generation (i.e., a nonlinear transfer of energy from the long vertically propagating waves to shorter modes).

Wavelet spectrum analysis approach to model validation of dynamic systems

Feature-based validation techniques for dynamic system models could be unreliable for nonlinear, stochastic, and transient dynamic behavior, where the time series is usually non-stationary. This paper presents a wavelet spectral analysis approach to validate a computational model for a dynamic system. Continuous wavelet transform is performed on the time series data for both model prediction and experimental observation using a Morlet wavelet function. The wavelet cross-spectrum is calculated for the two sets of data to construct a time–frequency phase difference map. The Box-plot, an exploratory data analysis technique, is applied to interpret the phase difference for validation purposes. In addition, wavelet time–frequency coherence is calculated using the locally and globally smoothed wavelet power spectra of the two data sets. Significance tests are performed to quantitatively verify whether the wavelet time-varying coherence is significant at a specific time and frequency point, considering uncertainties in both predicted and observed time series data. The proposed wavelet spectrum analysis approach is illustrated with a dynamics validation challenge problem developed at the Sandia National Laboratories. A comparison study is conducted to demonstrate the advantages of the proposed methodologies over classical frequency-independent cross-correlation analysis and time-independent cross-coherence analysis for the validation of dynamic systems.

Cross wavelet analyses of annual continental freshwater discharge and selected climate indices

Summary It is now well recognized that large scale atmospheric and oceanic circulations fluctuations have a strong impact on the global hydrological cycle. Because of the complexity of the hydrological processes over continental surfaces, it is often proposed to deduce this variability from insightful analysis of river discharge time series since it integrates a large number of climatological parameters such as precipitation, temperature and evapotranspiration but also land cover evolutions. However, up to now these studies remain restricted to basin or regional scale and no larger scale of these relationships between climate and continental hydrology has yet been proposed. Such relationships are helpful in the global understanding of the non-stationary relationships that exist between ocean and atmosphere mean conditions and freshwater discharge integrated at a continental scale. Based on a recent estimation of annual continental freshwater discharge over the 1876–1994 interval, a cross wavelet analysis (including cross wavelet spectrum and wavelet coherence) together with selected climate indices (North Atlantic Oscillation – NAO, Arctic Oscillation – AO, Southern Oscillation Index – SOI, Pacific Decadal Oscillation – PDO and NINO3.4 – Pacific mean Sea Surface Temperature) is exposed. The relationships are characterised by a high temporal unstationarity but three main bands of variability are identified and analyzed: 2–10-year, 10–20-year and 20–30-year variability. The five continents exhibit a temporal correlation with the five indexes sometimes on the entire interval but more often on restricted intervals. NAO and AO impact the 4–15-year variability of the five continents discharge. SOI impacts the 2–7-year variability of all continent discharge variability except Europe. NINO3.4 impacts the 2–8-year variability of Africa, Asia and South America discharge but also the 10–20-year variability of Africa, Asia, North America and South America discharge variability. Finally, PDO impacts the ∼10–30-year variability of Asia, Europe, North America and South America discharge variability. These results could allow a first order prediction of the future evolutions of continental water resources from a climate change point of view in relationship with climate scenarios of evolution of atmospheric and sea surface temperature conditions.

Cross-wavelet transform as a new paradigm for feature extraction from noisy partial discharge pulses

In this work a new approach based on cross-wavelet transform towards identification of noisy Partial Discharge (PD) patterns has been proposed. Different partial discharge patterns are recorded from the various samples prepared with known defects. A novel cross-wavelet transform based technique is used for feature extraction from raw noisy partial discharge signals. Noise is a significant problem in PD detection. The proposed method eliminates the requirement of denoising prior to processing and therefore it can be used to develop an automated and intelligent PD detector that requires minimal human expertise during its operation and analysis. A rough-set theory (RST) based classifier is used to classify the extracted features. Results show that the partial discharge patterns can be classified properly from the noisy waveforms. The effectiveness of the feature extraction methodology has also been verified with two other commonly used classification techniques: Artificial Neural Network (ANN) based classifier and Fuzzy classifier. It is found that the type of defect within insulation can be classified efficiently with the features extracted from cross-wavelet spectra of PD waveforms by all of these methods with a reasonable degree of accuracy.