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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: Although there exists an infinite variety of wavelet transformations, 22 orthonormal wavelet transforms that are typically used, which include Haar, 9 daublets, 5 coiflets, and 7 symmlets, were evaluated and four threshold selection methods have been studied.
Abstract: Discrete wavelet transform (DWT) denoising contains three steps: forward transformation of the signal to the wavelet domain, reduction of the wavelet coefficients, and inverse transformation to the native domain. Three aspects that should be considered for DWT denoising include selecting the wavelet type, selecting the threshold, and applying the threshold to the wavelet coefficients. Although there exists an infinite variety of wavelet transformations, 22 orthonormal wavelet transforms that are typically used, which include Haar, 9 daublets, 5 coiflets, and 7 symmlets, were evaluated. Four threshold selection methods have been studied: universal, minimax, Stein's unbiased estimate of risk (SURE), and minimum description length (MDL) criteria. The application of the threshold to the wavelet coefficients includes global (hard, soft, garrote, and firm), level-dependent, data-dependent, translation invariant (TI), and wavelet package transform (WPT) thresholding methods. The different DWT-based denoising m...

81 citations

Journal ArticleDOI
TL;DR: A simple alternative procedure to reduce leakage in the Fourier spectrum of a periodic signal is proposed and results obtained are empirically analyzed and compared with those given by an instrument with built-in FFT capabilities.
Abstract: The Fourier spectrum of a periodic signal may be obtained by fast Fourier transform algorithms, but, as is well known, special care must be taken to avoid severe distortions introduced by the sampling process. The main problem is the leakage generated by the truncation required to obtain a finite length sampled data. The usual procedure to reduce leakage is to multiply the sampled signal by a weighting window. Several kinds of windows have been proposed in the literature, and today they are also included in many commercial instruments. A simple alternative procedure is proposed in this paper. It is implemented with a PC compatible data acquisition board (DAQ) and consists of an algorithm that uses decimation and interpolation techniques. This algorithm is equivalent to the use of an adjustable sampling frequency and correspondingly an adjustable window size. Results obtained by this method on both harmonic and polyharmonic signals are empirically analyzed and compared with those given by an instrument with built-in FFT capabilities.

81 citations

Journal ArticleDOI
TL;DR: An automatic method for three-dimensional (3-D) shape recognition that combines the Fourier transform profilometry technique with a real-time recognition setup such as the joint transform correlator (JTC).
Abstract: An automatic method for three-dimensional (3-D) shape recognition is proposed. It combines the Fourier transform profilometry technique with a real-time recognition setup such as the joint transform correlator (JTC). A grating is projected onto the object surface resulting in a distorted grating pattern. Since this pattern carries information about the depth and the shape of the object, their comparison provides a method for recognizing 3-D objects in real time. A two-cycle JTC is used for this purpose. Experimental results demonstrate the theory and show the utility of the new proposed method.

80 citations

Journal ArticleDOI
TL;DR: This new bandpass matched filter shows improved discrimination capability with respect to the conventional matched filter and improved signal-to-noise ratio withrespect to the phase-only matched filter.
Abstract: A shift-invariant optical continuous wavelet transform is used for pattern recognition. We propose an optical wavelet matched filter that performs optical wavelet transforms for edge enhancement and the correlation between two wavelet transforms in a single step. This new bandpass matched filter shows improved discrimination capability with respect to the conventional matched filter and improved signal-to-noise ratio with respect to the phase-only matched filter. The wavelet matched filter provides flexibility of an adaptive choice of the scale factors of the wavelets that permit the selection of size and orientation of the smoothing function used in edge enhancement and the optimization of the performance of the filter. Optical experimental results are shown.

80 citations

Journal ArticleDOI
TL;DR: This paper suggests a generalization of the Hartley transformation based on the fractional Fourier transform, coined it “fractional Hartley transform (FHT)” and additional useful transformations used for signal processing are discussed.

80 citations


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