Topic
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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15 Jul 2002
TL;DR: The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance as discussed by the authors is a comprehensive overview of wavelet transform applications in science, engineering, medicine and finance.
Abstract: (The correction deals with the fact that the complex Morlet wavelet has a non-zero See for example: The Illustrated Wavelet Transform Handbook: Introductory. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance. CRC Press, Boca Raton. Tags: synchrosqueezing time-frequency analysis wavelet transform P.S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory.
942 citations
TL;DR: This paper constructs translation-invariant operators on L 2 .R d /, which are Lipschitz-continuous to the action of diffeomorphisms, and extendsScattering operators are extended on L2 .G/, where G is a compact Lie group, and are invariant under theaction of G.
Abstract: This paper constructs translation-invariant operators on L 2 .R d /, which are Lipschitz-continuous to the action of diffeomorphisms. A scattering propagator is a path-ordered product of nonlinear and noncommuting operators, each of which computes the modulus of a wavelet transform. A local integration defines a windowed scattering transform, which is proved to be Lipschitz-continuous to the action of C 2 diffeomorphisms. As the window size increases, it converges to a wavelet scattering transform that is translation invariant. Scattering coefficients also provide representations of stationary processes. Expected values depend upon high-order moments and can discriminate processes having the same power spectrum. Scattering operators are extended on L 2 .G/, where G is a compact Lie group, and are invariant under the action of G. Combining a scattering on L 2 .R d / and on L 2 .SO.d// defines a translation- and rotation-invariant scattering on L 2 .R d /. © 2012 Wiley Periodicals, Inc.
941 citations
01 Apr 1996
TL;DR: In this article, the authors present a new approach to detect, localize, and investigate the feasibility of classifying various types of power quality disturbances using dyadic-orthonormal wavelet transform analysis.
Abstract: In this paper we present a new approach to detect, localize, and investigate the feasibility of classifying various types of power quality disturbances. The approach is based on wavelet transform analysis, particularly the dyadic-orthonormal wavelet transform. The key idea underlying the approach is to decompose a given disturbance signal into other signals which represent a smoothed version and a detailed version of the original signal. The decomposition is performed using multiresolution signal decomposition techniques. We demonstrate and test our proposed technique to detect and localize disturbances with actual power line disturbances. In order to enhance the detection outcomes, we utilize the squared wavelet transform coefficients of the analyzed power line signal. Based on the results of the detection and localization, we carry out an initial investigation of the ability to uniquely characterize various types of power quality disturbances. This investigation is based on characterizing the uniqueness of the squared wavelet transform coefficients for each power quality disturbance.
908 citations
TL;DR: The 2-D orthogonal wavelet transform decomposes images into both spatial and spectrally local coefficients and gave high to acceptable quality reconstruction at compression ratios for the Miss America and Lena monochrome images.
Abstract: The 2-D orthogonal wavelet transform decomposes images into both spatial and spectrally local coefficients. The transformed coefficients were coded hierarchically and individually quantized in accordance with the local estimated noise sensitivity of the human visual system (HVS). The algorithm can be mapped easily onto VLSI. For the Miss America and Lena monochrome images, the technique gave high to acceptable quality reconstruction at compression ratios of 0.3-0.2 and 0.64-0.43 bits per pixel (bpp), respectively. >
857 citations