scispace - formally typeset
Search or ask a question

Showing papers on "Harmonic wavelet transform published in 1994"


Journal ArticleDOI
TL;DR: Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains.
Abstract: A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.

499 citations


Proceedings ArticleDOI
13 Nov 1994
TL;DR: In the image fusion scheme presented in this paper, the wavelet transforms of the input images are appropriately combined, and the new image is obtained by taking the inverse wavelet transform of the fused wavelet coefficients.
Abstract: In the image fusion scheme presented in this paper, the wavelet transforms of the input images are appropriately combined, and the new image is obtained by taking the inverse wavelet transform of the fused wavelet coefficients. An area-based maximum selection rule and a consistency verification step are used for feature selection. A performance measure using specially generated test images is also suggested. >

422 citations


Journal ArticleDOI
TL;DR: In this article, the wavelet transform is applied to the detection of a damaged tooth in a spur gear in a sparsified gear and a fault detection algorithm is presented, based on a similarity analysis of patterns obtained from the modulus of the Wavelet transform.

243 citations


Journal ArticleDOI
TL;DR: The Radon-Wigner transform as mentioned in this paper is the squared modulus of the fractional Fourier transform, and it can be used to translate signal and image processing results between different signal representations.
Abstract: Two recently described transforms are shown to be related. The Radon–Wigner transform is the squared modulus of the fractional Fourier transform. This new theorem may serve to translate signal and image processing results between different signal representations. Some consequences regarding moments are presented, including a new fractional-Fourier-transform uncertainty relation. Implications for processing are suggested.

211 citations


Journal ArticleDOI
TL;DR: It now appears technically feasible to filter and decompose EEG using wavelet transforms in real time with ordinary microprocessors, without compromising the accuracy of feature extraction.

208 citations


Book ChapterDOI
01 Jan 1994
TL;DR: The Fourier Transform representation for functions whose inputs are boolean has been far less studied, but it seems that it can be used to learn many classes of boolean functions.
Abstract: The importance of using the “right” representation of a function in order to “approximate” it has been widely recognized. The Fourier Transform representation of a function is a classic representation which is widely used to approximate real functions (i.e. functions whose inputs are real numbers). However, the Fourier Transform representation for functions whose inputs are boolean has been far less studied. On the other hand it seems that the Fourier Transform representation can be used to learn many classes of boolean functions.

204 citations


Journal ArticleDOI
TL;DR: Presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation, and proposes orthogonal and periodic basic discrete wavelets to get a correct invertibility of this procedure.
Abstract: Presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation. This is done by defining a purely invertible discrete transform, representing a signal either in the time or in the time-frequency domain, as simply as possible with the conventional discrete Fourier transform between the time and the frequency domains. The wavelet concept has been used to build this transform. To get a correct invertibility of this procedure, the authors have proposed orthogonal and periodic basic discrete wavelets. The properties of such a transform are described, and examples on brain-evoked potential signals are given to illustrate the time-frequency filtering possibilities. >

194 citations


Book
01 Jul 1994
TL;DR: This text provides a clear, comprehensive presentation of both the theory and applications in signals, systems, and transforms, including the Fourier transform,The Fourier series, the Laplace transform, the discrete-time and the discrete Fourier transforms, and the z-transform.
Abstract: For sophomore/junior-level signals and systems courses in Electrical and Computer Engineering departments. This text provides a clear, comprehensive presentation of both the theory and applications in signals, systems, and transforms. It presents the mathematical background of signals and systems, including the Fourier transform, the Fourier series, the Laplace transform, the discrete-time and the discrete Fourier transforms, and the z-transform. The text integrates MATLAB examples into the presentation of signal and system theory and applications.

190 citations


Journal ArticleDOI
TL;DR: A tutorial introduction to the theory, implementation and interpretation of the wavelet transform to the time-scale (time-frequency) analysis of discrete signals.
Abstract: Wavelets and wavelet transforms are a relatively new topic in signal processing. Their development and, in particular, their application remains an active area of research. This paper presents a tutorial introduction to the theory, implementation and interpretation of the wavelet transform. The paper concentrates on the application of the wavelet transform to the time-scale (time-frequency) analysis of discrete signals. Examples are given of the analysis of basic test signals and of an actual electrocardiographic signal.< >

159 citations


Journal ArticleDOI
TL;DR: The “fractional Fourier transform,” previously developed by the authors, is applied to this problem with a substantial savings in computation.
Abstract: The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems often requires a large FFT to be performed, even though most of the input data to this FFT may be zero and only a small fraction of the output data may be of interest. In this note, the “fractional Fourier transform,” previously developed by the authors, is applied to this problem with a substantial savings in computation.

141 citations


Journal ArticleDOI
TL;DR: A new complete and convergent set of invariant features under planar similarities is proposed using the Analytical Fourier-Mellin Transform (AFMT), which gives a distance between the shapes which is invariant under similarities.

Journal ArticleDOI
TL;DR: In this article, the application of the fractional Fourier transform to optical propagation problems is discussed, and the conceptual and practical advantages of this new formulation are noted, as well as the theoretical advantages of the new formulation.
Abstract: The application of the fractional Fourier transform to optical propagation problems is discussed. As illustrative examples, diffraction in a free medium as well as propagation through optical fibres are analysed with the fractional Fourier transform formalism. The conceptual and practical advantages of this new formulation are noted.

Journal ArticleDOI
TL;DR: A new approach for filtering based on the wavelet transform is presented, and several algorithms are proposed, and a criterion of quality, which takes into account the resolution, is used to compare these algorithms.

Journal ArticleDOI
TL;DR: An iterative algorithm for signal recovery from discrete-time wavelet transform maxima is presented by using the method of projections onto convex sets and convergence of the algorithm is assured.
Abstract: The paper presents an iterative algorithm for signal recovery from discrete-time wavelet transform maxima. The signal recovery algorithm is developed by using the method of projections onto convex sets. Convergence of the algorithm is assured. >

Journal ArticleDOI
TL;DR: A simulation study illustrates the artifacts of every time-frequency representation on pure sinusoids and gives performance evaluation of the different methods when searching a sinusoid embedded in a QRS complex.
Abstract: The main transforms of Cohen's class allow signal representation simultaneously in time and frequency domains. Wavelet transforms make it possible to link the temporal window width to the analyzing frequency and leads to a "modified wavelet transform" which improves resolution both in time and frequency. A simulation study illustrates the artifacts of every time-frequency representation on pure sinusoids and gives performance evaluation of the different methods when searching a sinusoid embedded in a QRS complex. Analyses of real signals from healthy and pathological subjects confirm the simulation results and complete the characterization of ventricular late potentials yet detected by signal averaging. >

Journal ArticleDOI
TL;DR: The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform, providing new insight into wave propagation and spherical mirror resonators.
Abstract: The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting the fractional Fourier transform as a mathematical tool in analyzing such systems.

Journal ArticleDOI
TL;DR: The slope transform is presented, which provides tangential morphology with the analytical power which the Fourier tansform lends to linear signal processing, in particular: dilation becomes addition (just as under a Fourier transform, convolution becomes multiplication).

Patent
13 Jan 1994
TL;DR: In this paper, a method for decomposing signals into efficient time-frequency representations for data compression and recognition which uses adaptable wavelet basis functions and concentrates a signal or image's information to a higher degree than methods based on the discrete Fourier transform, the discrete cosine transform and known adaptive transform techniques is presented.
Abstract: A method for decomposing signals into efficient time-frequency representations for data compression and recognition which uses adaptable wavelet basis functions and concentrates a signal or image's information to a higher degree than methods based on the discrete fourier transform, the discrete cosine transform, the standard wavelet transform and known adaptive transform techniques. The purpose of the present invention is to enable data signals and images to be stored and transmitted very efficiently. The time-frequency plane is broken up into subspaces. The method determines the optimum basis function for each of the subspace regions. Basis functions are chosen such that much of the information in the signal is contained in a small number of coefficients. The resulting coefficients form a set that represents the signal in the most concentrated manner.

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.

Journal ArticleDOI
TL;DR: In this paper, the wavelet transform is applied to the analysis of transient waves propagating in a dispersive medium, and the similarity in the fundamental characteristics of the analysis tool and the physical phenomena are exploited during the decomposition of the measured signals.
Abstract: The wavelet transform is applied to the analysis of transient waves propagating in a dispersive medium. Experimental techniques are employed to measure the transient flexural vibrations of an impact excited uniform beam. The similarity in the fundamental characteristics of the analysis tool and the physical phenomena are exploited during the decomposition of the measured signals. The wavelet transform of the acceleration response resulted in a time‐scale representation which provided a clear exposition of the time evolution of the spectral components during the dispersion process. The relation between the wavelet transform and the group properties of the dispersed waveform are emphasized. In the applications to finite systems, the efficacy of the wavelet transform is demonstrated by analyzing complex transient wave‐interference patterns which evolve over wide spectral ranges. An interesting periodic pulse reformation phenomena is uncovered on a uniform beam with free boundaries. Following the dispersion and the multiple reflections of the bending waves, the original impulsive waveform is found to be reconstituted periodically in time. Based on the physical examples, the advantages and shortcomings of the wavelet transform are discussed.

Journal ArticleDOI
TL;DR: Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented and approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency.
Abstract: Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by convolving a premodulated signal with a Gaussian-like window and demodulating the output. The window functions are either B-splines dilated by an integer factor m or quasi-Gaussians of arbitrary size generated from the n-fold convolution of a symmetrical exponential. Both approaches result in a recursive implementation with a complexity independent of the window size (O(N)). >

Journal ArticleDOI
TL;DR: The authors show that making use of the discrete wavelet transform to analyse data implies performing a preliminary initialization of the fast pyramidal algorithm, and an approximation enabling easy performance is proposed.
Abstract: The authors show that making use of the discrete wavelet transform to analyse data implies performing a preliminary initialization of the fast pyramidal algorithm. An approximation enabling easy performance of such an initialization is proposed. >

Proceedings ArticleDOI
13 Nov 1994
TL;DR: This work proposes a novel method based on wavelet thresholding for enhancement of decompressed transform coded images that works remarkably well in "deblocking" of DCT compressed images.
Abstract: We propose a novel method based on wavelet thresholding for enhancement of decompressed transform coded images. Transform coding at low bit rates typically introduces artifacts associated with the basis functions of the transform. In particular, the method works remarkably well in "deblocking" of DCT compressed images. The method is nonlinear, computationally efficient, and spatially adaptive and has the distinct feature that it removes artifacts yet retain sharp features in the images. An important implication of this result is that images coded using the JPEG standard can efficiently be postprocessed to give significantly improved visual quality in the images. The algorithm can use a conventional JPEG encoder and decoder for which VLSI chips are available. >

Proceedings ArticleDOI
25 Oct 1994
TL;DR: In this article, the performance of a multiresolution-based transient detector using analytic wavelets has been studied and compared with one based on a continuous wavelet transform, as well as with other standard methods and show that wavelets perform best when the transients are superimposed on a colored 1/f background noise.
Abstract: Designs and studies the performance of a multiresolution-based transient detector. The transients the authors are interested in consist of wide-band, pulse-like, coherent structures in a turbulent flow. To take advantage of the fast pyramidal wavelet algorithm, an important point when processing large amounts of experimental data, the detector makes use of the discrete wavelet transform. The authors show how the lack of time-invariance drawback of the discrete transform can be efficiently overcome by using relevant analytic wavelets. They thus compare this detection technique with one based on a continuous wavelet transform, as well as with other standard methods and show that wavelets perform best when the transients are superimposed on a colored 1/f background noise. This description is very close to that of turbulence and relevant also in many other situations. >

Journal ArticleDOI
TL;DR: In this paper, a simple relation between the fractional Fourier transform (FRACFT) and the Green's function for the harmonic oscillator is demonstrated, which enables us to understand easily the characteristics of FRACFT.

Proceedings ArticleDOI
01 Jan 1994
TL;DR: In this paper, the wavelet transform is applied to the analysis of ultrasonic waves for improved signal detection and analysis, and the results show good detection even when large white noise was added.
Abstract: The wavelet transform is applied to the analysis of ultrasonic waves for improved signal detection and analysis. In instances where the mother wavelet is well defined, the wavelet transform has relative insensitivity to noise and does not need windowing. Peak detection of ultrasonic pulses using the wavelet transform is described and results show good detection even when large white noise was added. The use of the wavelet transform to extract the frequency dispersion relation of the Lamb wave velocity is also described. The two-dimensional wavelet transform allows for both time and frequency analysis, thus making it particularly suitable for dispersion studies. Experimental and numerical results show the superior performance of the wavelet transform signal processor

Proceedings ArticleDOI
15 Mar 1994
TL;DR: In this paper, the authors developed outlier resistant wavelet transforms, in which outliers and outlier patches are localized to just a few scales, and improved upon the Donoho and Johnstone nonlinear signal extraction methods.
Abstract: In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transform, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the 'S+WAVELETS' object-oriented toolkit for wavelet analysis.

Proceedings ArticleDOI
13 Nov 1994
TL;DR: Experimental results demonstrate the flexibility to selectively enhance features of different sizes and ability to control noise magnification of the new multiscale gradient transformation method.
Abstract: We present a new technique for image contrast enhancement via multiscale gradient transformation In contrast to histogram-based techniques which aim to change the global statistical distribution of pixel intensities, we improve image contrast by modifying the modulus of the gradient image at multiple scales In computation, a multiscale gradient representation of the image is generated by a wavelet transform (WT) Linear or nonlinear transformation is applied to multiscale gradients A contrast-enhanced image is obtained from the transformed multiscale gradients by the inverse wavelet transform Experimental results demonstrate two advantages of the new method: its flexibility to selectively enhance features of different sizes and ability to control noise magnification >

Journal ArticleDOI
TL;DR: In this paper, a split for the wavelet transform and merge for the inverse transform are presented for finite-duration discrete-time signals of arbitrary length not restricted to a power of 2.
Abstract: The algorithms split for the wavelet transform and merge for the inverse wavelet transform are presented for finite-duration discrete-time signals of arbitrary length not restricted to a power of 2. Alternative matrix- and vector-filter implementations of alternative truncated, circulant, and extended versions are discussed. Matrix- and vector-filter implementations yield identical results and enhance, respectively, didactic conceptualization and computational efficiency. Truncated, circulant, and extended versions produce the signal-end effects of, respectively, errors, periodization, and redundancy in the transform coefficients. The use of any one of these three versions avoids the signal-end effects associated with the other two versions. Additional alternatives that eliminate all signal-end effects (albeit at the cost of increased algorithmic complexity) are discussed briefly