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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.


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Journal ArticleDOI
TL;DR: The base 8 algorithms described in this paper allow one to perform as many base 8 iterations as possible and then finish the computation by performing a base 4 or a base 2 iteration if one is required, which preserves the versatility of the base 2 algorithm while attaining the computational advantage of thebase 8 algorithm.
Abstract: 1. Introduction. Cooley and Tukey stated in their original paper [1] that the Fast Fourier Transform algorithm is formally most efficient when the number of samples in a record can be expressed as a power of 3 (i.e., N = 3m), and further that there is little efficiency lost by using N = 2m or N = 4™. Later, however, it was recognized that the symmetries of the sine and cosine weighting functions made the base 4 algorithms more efficient than either the base 2 or the base 3 algorithms [2], [3]. Making use of this observation, Gentleman and Sande have constructed an algorithm which performs as many iterations of the transform as possible in a base 4 mode, and then, if required, performs the last iteration in a base 2 mode. Although this "4 + 2" algorithm is more efficient than base 2 algorithms, it is now apparent that the techniques used by Gentleman and Sande can be profitably carried one step further to an even more efficient, base 8 algorithm. The base 8 algorithms described in this paper allow one to perform as many base 8 iterations as possible and then finish the computation by performing a base 4 or a base 2 iteration if one is required. This combination preserves the versatility of the base 2 algorithm while attaining the computational advantage of the base 8 algorithm.

88 citations

Proceedings ArticleDOI
16 May 2005
TL;DR: In this article, a wavelet-packet transform (WPT) was proposed to decompose the voltage/current waveforms into uniform frequency bands corresponding to the odd harmonic components of the signal, and the results obtained using DFT analysis and the harmonic group concept introduced by the International Electrotechnical Commission using different test waveforms proposed in standard IEC-61000-4-7.
Abstract: The paper proposes an algorithm based on the wavelet-packet transform for the analysis of harmonics in power systems. The algorithm proposed decomposes the voltage/current waveforms into uniform frequency bands corresponding to the odd harmonic components of the signal. First, the selection of the mother wavelet, the sampling frequency and the frequency characteristics of the selected wavelet filter bank are studied. Finally the performance of the method proposed is compared with the results obtained using DFT analysis and the harmonic group concept introduced by the International Electrotechnical Commission using different test waveforms proposed in standard IEC-61000-4-7

88 citations

Journal ArticleDOI
TL;DR: The scale invariance of the Mellin transform and its optical synthesis in real-time are discussed in this article, where a scale invariant correlation and a combined Fourier-Mellin transform that is both scale and shift invariant are discussed.
Abstract: The scale invariance of the Mellin transform and its optical synthesis in real-time are discussed. An initial off-line demonstration of an optical Mellin transform is presented. A scale invariant correlation and a combined Fourier-Mellin transform that is both scale and shift invariant are discussed. Applications of these transforms in optical data processing and optical pattern recognition are emphasized.

87 citations

Journal ArticleDOI
TL;DR: This work allows the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled.
Abstract: We provide a general treatment of optical two-dimensional fractional Fourier transforming systems. We not only allow the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled. We further discuss systems that do not allow all these parameters to be controlled at the same time but are simpler and employ a fewer number of lenses. The variety of systems discussed and the design equations provided should be useful in practical applications for which an optical fractional Fourier transforming stage is to be employed.

87 citations


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