This paper presents a wavelet analysis technique together with support vector machines (SVM) to discriminate partial discharges (PD) from external disturbances (electromagnetic noise) in a GIS PD measuring system based on magnetic antennas. The technique uses the Cross Wavelet Transform (XWT) to process the PD signals and the external disturbances coming from the magnetic antennas installed in the GIS compartments. The measurements were performed in a high voltage (HV) GIS containing a source of PD and common-mode external disturbances, where the external disturbances were created by an electric dipole radiator placed in the middle of the GIS. The PD were created by connecting a needle to the main conductor in one of the GIS compartments. The cross wavelet transform and its local relative phase were used for feature extraction from the PD and the external noise. The features extracted formed linearly separable clusters of PD and external disturbances. These clusters were automatically classified by a support vector machine (SVM) algorithm. The SVM presented an error rate of 0.33%, correctly classifying 99.66% of the signals. The technique is intended to reduce the PD false positive indications of the common-mode signals created by an electric dipole. The measuring system fundamentals, the XWT foundations, the features extraction, the data analysis, the classification algorithm, and the experimental results are presented.

Abstract. Interpretation of land subsidence time-series to understand the evolution of the phenomenon and the existing relationships between triggers and measured displacements is a great challenge. Continuous wavelet transform (CWT) is a powerful signal processing method mainly suitable for the analysis of individual nonstationary time-series. CWT expands time-series into the time-frequency space allowing identification of localized nonstationary periodicities. Complementarily, Cross Wavelet Transform (XWT) and Wavelet Coherence (WTC) methods allow the comparison of two time-series that may be expected to be related in order to identify regions in the time-frequency domain that exhibit large common cross-power and wavelet coherence, respectively, and therefore are evocative of causality. In this work we use CWT, XWT and WTC to analyze piezometric and InSAR (interferometric synthetic aperture radar) time-series from the Tertiary aquifer of Madrid (Spain) to illustrate their capabilities for interpreting land subsidence and piezometric time-series information.

Este estudo mostra uma análise em transformada em ondeleta cruzada e coerência em ondeleta aplicada a duas séries temporais, sendo uma delas precipitação e a outra temperatura do ar. O objetivo deste estudo é mostrar que esta técnica é uma ferramenta poderosa na análise de séries temporais climáticas, para isso à aplicamos a duas séries com relação física muito conhecida na climatologia. Além da aplicação realizada, recorreu-se também a uma descrição matemática dos métodos. A técnica da transformada em ondeletas cruzada e coerência mostrou-se eficiente em capturar a relação matemática entre as séries de precipitação e temperatura do ar. Com este estudo esperamos difundir o uso desta técnica para fins de ensino e pesquisa em diversos sistemas geofísicos. Analysis of Climate Data Using Transformed Crosswave and Coherence A B S T R A C TThis study presents a cross wavelet transform and wavelet coherence analysis applied to a precipitation and an air temperature time series. The objective of this study is to demonstrate that this technique is a powerful tool in the analysis of climatic time series, and can be applied to two time series with very well-known physical relationships in terms of climatology. In addition to this application, a mathematical description of the methods was done. The cross-curves and coherence technique proved to be efficient in capturing the mathematical relationship between precipitation series and air temperature. With this study we hope to disseminate the use of this technique for teaching and research purposes in various geophysical systems.Keywords: Phase Angle, Wavelet Coherence, Cross wavelet, Precipitation, Temperature. 

Observations show that the Sun, which is the primary source of energy for the Earth’s climate system, is a variable star. In order to understand the influence of solar variability on the Earth’s climate, knowledge of solar variability and solar–terrestrial interactions is required. Knowledge of the Sun’s cyclic behavior can be used for future prediction purposes on Earth. In this study, the possible connection between sunspot numbers (SSN) as a proxy for the 11-year solar cycle and mean annual precipitation (MAP) in Iran were investigated, with the motivation of contributing to the controversial issue of the relationship between SSN and MAP. Nine locations throughout Iran were selected, representing different climatic conditions in the country. Cross-wavelet transform (XWT) analysis was employed to investigate the temporal relationship between cyclicities in SSN and MAP. Results indicated that a distinct 8–12-year correlation exists between the two time series of SSN and MAP, and peaks in precipitation mostly occur one to three years after the SSN maxima. The findings of this study can be beneficial for policymakers, to consider future potential droughts and wet years based on sunspot activities, so that water resources can be more properly managed.

The spatiotemporal variability of snow depth supplies important information for snow disaster prevention. The monthly and annual snow depths and weather data (from Xinjiang Meteorological Observatory) at 102 meteorological stations in Xinjiang, China over 1961–2015 were used to analyze the spatiotemporal characteristics of snow depths from different aspects. The empirical orthogonal function (EOF), the modified Mann–Kendall method, Morlet wavelet, Daubechies wavelet decomposition and cross wavelet transform were applied to investigate the trend and significance, spatial structure, periods, decomposed series and coherence of monthly and annual snow depths. The results indicated that: (1) The value of EOF first spatial mode (EOF1) of the monthly and annual snow depths in north Xinjiang were larger than south Xinjiang, indicating greater variability of snow depths in north Xinjiang. (2) The change points of annual snow depth mainly occurred during 1969–1979 and 1980–1990. The annual snow depth of most sites showed increasing trends, but with different slope magnitudes. (3) The sites that had main periods of 2–8 and 9–14 years of monthly and annual snow depths (detected by the Morlet wavelet) mainly distributed in northern Xinjiang. The sites that had main periods of 15–20 years of monthly and annual snow depths mainly distributed in southwestern Xinjiang. (4) By using the Daubechies wavelet, the decomposed annual snow depth in entire Xinjiang tended to increase. (5) Through the cross wavelet transform, annual snow depths in entire Xinjiang had good correlations with annual precipitation or relative humidity, and showed a low negative correlation with minimum temperature or sunshine hours. In conclusion, the monthly and annual snow depths had comprehensive spatiotemporal variability but had overall increasing trend during 1961–2015.

Two complementary aspects of interpersonal entrainment – synchronization and movement coordination – are explored in North Indian classical instrumental music, in the auditory and visual domains respectively. Sensorimotor synchronization (SMS) is explored by analysing pairwise asynchronies between the event onsets of instrumental soloists and their tabla accompanists, and the variability of asynchrony by factors including tempo, dynamic level and metrical position is explored. Movement coordination is quantified using cross wavelet transform (CWT) analysis of upper body movement data, and differences in CWT Energy are investigated in relation to the metrical and cadential structures of the music. The analysis demonstrates that SMS within this corpus varies significantly with tempo, event density, peak levels and leadership. Effects of metrical position on pairwise asynchrony are small and offer little support for the hypothesis of lower variability in synchronization on strong metrical positions; a larger difference was found at cadential downbeats, which show increased melody lead. Movement coordination is greater at metrical boundaries than elsewhere, and most strikingly is greater at cadential than at other metrical downbeats. The implications of these findings for understanding performer coordination are discussed in relation to ethnographic research on the genre.