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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TL;DR: In this article, a new representation of the Schrodinger operator of a free particle by using the short-time Fourier transform was proposed, and its applications were described. But this representation is restricted to the case of a single particle.
Abstract: We propose a new representation of the Schrodinger operator of a free particle by using the short-time Fourier transform and give its applications.
38 citations
TL;DR: In this article, a continuous wavelet transform (CWT) approach is proposed to generate spectrum-compatible records from the modification of acceleration time histories recorded in actual seismic events, and the computational efficiency is increased greatly by performing the wavelet decomposition and details reconstruction via fast convolution using fast Fourier transforms.
Abstract: The seismic design of most civil structures is usually accomplished using the response spectrum approach or simplified equivalent lateral force methods. However, some special tasks require the use of dynamic time history analyses. In the nuclear industry, for example, dynamic analyses are required in the design verification and seismic assessment of critical buildings and in the development of floor response spectra and free-field ground response spectra. The input motion for these analyses requires acceleration time series whose response spectrum matches a target design spectrum. This article revises the continuous wavelet transform (CWT) approach to generate spectrum-compatible records from the modification of acceleration time histories recorded in actual seismic events. The computational efficiency of the algorithm is increased greatly by performing the wavelet decomposition and details reconstruction via fast convolution using fast Fourier transforms. The new algorithm is evaluated using a typical design spectrum from the nuclear industry and different seed records.
38 citations
01 Jan 2017
TL;DR: The wavelet transform is a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals.
Abstract: Historically, the concept of wavelets started to appear more frequently only in the early 1980s. This new concept can be viewed as a synthesis of various ideas originating from different disciplines including mathematics, physics, and engineering. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean Morlet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. Wavelet transforms are relatively recent developments that have fascinated the scientific, engineering, and mathematics community with their versatile applicability. The application areas for wavelets have been growing for the last 20 years at a very rapid rate. They have been applied in a number of fields including signal and image processing, sampling theory, turbulence, differential equations, statistics, quality control, computer graphics, economics and finance, medicine, neural networks, geophysics, astrophysics, quantum mechanics, neuroscience, and chemistry. For more information about the history and applications of wavelet transforms, the reader is referred to Daubechies (1992), Chui (l992), Meyer (1993a,b), Kaiser (1994), Cohen (1995), Hubbard (1996), Strang and Nguyen (1996), Burrus et al. (1997), Wojtaszczyk (1997), Debnath (1998a,b,c), Mallat (1998), Pinsky (2001), Ali et al. (2015), Gomes and Velho (2015), and Debnath and Shah (2015).
38 citations
01 Jan 2000
TL;DR: In this article, a new form of discrete wavelet transform was developed, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts.
Abstract: Recently we have developed a new form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2m:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. We analyse why the new transform can be designed to be shift invariant, and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this. (10 pages)
38 citations
Journal Article•
TL;DR: The test shows that this method can hold the information of the original images and enhance their detail information and is able to fusion rules based on wavelet transform.
Abstract: After analyzing some fusion rules based on wavelet transform and their effects,this paper presents a new method of image fusion.The test shows that this method can hold the information of the original images and enhance their detail information.
38 citations