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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the generalized S transform (GST) is generalized with two steps, and two kinds of new transforms are obtained, which are called generalized s transform (gST) and gST2.
Abstract: S transform (ST) proposed by Stockwell et al. is the unique transform that provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. This feature is very important for applications. However, the ST can't work well for seismic data analysis since its basic wavelet is not appropriate. In this paper, the ST is generalized with two steps, and two kinds of new transforms are obtained, which are called generalized S transform (GST). First, the basic wavelet in ST is replaced by a modulated harmonic wave with four undetermined coefficients, and then a new transform and its inverse are given, called GST1. Second, taking a linear combination of the basic wavelets in step 1 as a new basic wavelet, called GST2, and its inverse is constructed. To compare ST with GST, the ST and GST method are used to analyze several typical models of thin beds, respectively. The results show that the resolution of GST is better than that of ST. The GST method can determine accurately the location of interfaces of acoustic impedance in thin interbeds of thickness being only an eighth wavelength, while ST method can't. In this study, the effectiveness of GST method is also verified by processing results of real data.
92 citations
TL;DR: The complex-window S-transform is similar to a wavelet transform, but has the fixed phase reference of the Fourier transform, leading to better time frequency localization of similar waveforms on the time series.
92 citations
TL;DR: In this paper, the wavelet analysis technique is applied to analyze the frequency-domain electromagnetic backscattered signal from finite-size targets, which consists of both small-scale natural resonances and large-scale scattering center information.
Abstract: The wavelet analysis technique is applied to analyze the frequency-domain electromagnetic backscattered signal from finite-size targets. Since the frequency-domain radar echo consists of both small-scale natural resonances and large-scale scattering center information, the multiresolution property of the wavelet transform is well suited for analyzing such multiscale signals. Wavelet analysis examples of backscattered data from an open-ended waveguide cavity and a plasma cylinder are presented. Compared with the conventional short-time Fourier transform, the wavelet transform provides a more efficient representation of both the early-time scattering center data and the late-time resonances. The different scattering mechanisms are clearly resolved in the time-frequency representation. >
92 citations
01 Jun 1990
TL;DR: In this paper, the use of orthonormal bases of compactly supported wavelets to represent a discrete signal in 2 dimensions yields a localized representation of coefficient energy, and subsequent coding of the multiresolution representation is achieved through techniques such as scalar/vector quantization, hierarchical quantization and entropy coding to achieve compression.
Abstract: Multilevel unitary wavelet transform methods for image compression are described. The sub-band
decomposition preserves geometric image structure within each sub-band or level. This yields a multilevel
image representation. The use of orthonormal bases of compactly supported wavelets to represent a
discrete signal in 2 dimensions yields a localized representation of coefficient energy. Subsequent coding
of the multiresolution representation is achieved through techniques such as scalar/vector quantization,
hierarchical quantization, entropy coding, and non-linear prediction to achieve compression.
Performance advantages over the Discrete Cosine Transform are discussed. These include reduction of
errors and artifacts typical of Fourier-based spectral methods, such as frequency-domain quantization
noise and the Gibbs phenomenon. The wavelet method also eliminates distortion arising from data
blocking. The paper includes a quick review of past/present compression techniques, with special
attention paid to the Haar transfOrm, the simplest wavelet transform, and conventional Fourier-based subband
coding. Computational results are presented.
91 citations
TL;DR: In this article, it was shown that the truncation error can also be removed at discrete frequencies, simply by first subtracting a ramp from the step response of a network, with consequent noise enhancement.
Abstract: If the discrete Fourier transform of the step response of a network is taken, a large truncation error results, since only a finite number of samples is used. This error is usually removed by first differentiating the waveform, with consequent noise enhancement. The letter shows that the error may also be removed at discrete frequencies, simply by first subtracting a ramp from the step response.
91 citations