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Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.


Papers
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Journal ArticleDOI
TL;DR: The time-varying problem of wavelet transforms is addressed, and a new translation-invariant wavelet representation algorithm is proposed that can reduce the distortion substantially, if the input signals are transients that are sensitive to time shifts.
Abstract: We address the time-varying problem of wavelet transforms, and a new translation-invariant wavelet representation algorithm is proposed. Using the algorithm introduced by Beylkin (see SIAM J. Numer. Anal., vol. 29, p.1716-1740, 1992), we compute the wavelet transform for all the circular time shifts of a length-N signal in O(N log N) operations. The wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function. We apply the translation-invariant representation algorithm to a geoacoustic data compression application. The results show that the new algorithm can reduce the distortion (the squared error in our case) substantially, if the input signals are transients that are sensitive to time shifts.

149 citations

Journal ArticleDOI
TL;DR: In this article, an application of Morlet wavelets to the analysis of high-impedance fault generated signals is proposed in which the time and frequency information of a waveform can be presented as a visualized scheme.
Abstract: An application of Morlet wavelets to the analysis of high-impedance fault generated signals is proposed in this paper. With the time-frequency localization characteristics embedded in wavelets, the time and frequency information of a waveform can be presented as a visualized scheme. Different from the fast Fourier transform, the wavelet transform approach is more efficient in monitoring fault signals as time varies. The proposed method has been applied to discriminate the high-impedance faults from the normal switching events, and to examine the faults under various grounds including Portland cement, wet soil and grass. Testing results have demonstrated the practicality and advantages of the proposed method for the applications.

148 citations

Journal ArticleDOI
TL;DR: The Synchrosqueezing Transform (SST) as discussed by the authors is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques, which produces a well defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals.
Abstract: Time-frequency representation of seismic signals provides a source of information that is usually hidden in the Fourier spectrum. The short-time Fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components. Known limitations, such as trade-offs between time and frequency resolution, may be overcome by alternative techniques that extract instantaneous modal components. Empirical mode decomposition aims to decompose a signal into components that are well separated in the time-frequency plane allowing the reconstruction of these components. On the other hand, a recently proposed method called the “synchrosqueezing transform” (SST) is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques. This new tool produces a well-defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight ...

148 citations

Journal ArticleDOI
TL;DR: In this article, the authors compared wavelet filters and discrete short-time Fourier transform (DTFT) for power quality analysis on a power system consisting of 13 buses and is representative of a medium-sized industrial plant.

148 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202323
202274
20213
20207
20196
201831