Showing papers on "Continuous wavelet transform published in 1989"
TL;DR: The author describes the mathematical properties of such decompositions and introduces the wavelet transform, which relates to the decomposition of an image into a wavelet orthonormal basis.
Abstract: The author reviews recent multichannel models developed in psychophysiology, computer vision, and image processing. In psychophysiology, multichannel models have been particularly successful in explaining some low-level processing in the visual cortex. The expansion of a function into several frequency channels provides a representation which is intermediate between a spatial and a Fourier representation. The author describes the mathematical properties of such decompositions and introduces the wavelet transform. He reviews the classical multiresolution pyramidal transforms developed in computer vision and shows how they relate to the decomposition of an image into a wavelet orthonormal basis. He discusses the properties of the zero crossings of multifrequency channels. Zero-crossing representations are particularly well adapted for pattern recognition in computer vision. >
2,109 citations
TL;DR: This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ in terms of coherent states, focusing on Weyl–Heisenberg coherent states and affine coherent states.
Abstract: This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ in terms of coherent states. Two types of coherent states are considered: Weyl–Heisenberg coherent states, which arise from translations and modulations of a single function, and affine coherent states, called ’wavelets,’ which arise as translations and dilations of a single function. In each case it is shown how to represent any function in $L^2 ({\bf R})$ as a sum or integral of these states. Most of the paper is a survey of literature, most notably the work of I. Daubechies, A. Grossmann, and J. Morlet. A few results of the authors are included.
1,121 citations
Book•
01 Jan 1989
TL;DR: A real-time algorithm for Signal Analysis with the help of the Wavelet Transform is described in this paper. But it is not suitable for the use of the wavelet transform in computer vision applications.
Abstract: I Introduction to Wavelet Transforms.- Reading and Understanding Continuous Wavelet Transforms.- Orthonormal Wavelets.- Orthonormal Bases of Wavelets with Finite Support - Connection with Discrete Filters.- II Some Topics in Signal Analysis.- Some Aspects of Non-Stationary Signal Processing with Emphasis on Time-Frequency and Time-Scale Methods.- Detection of Abrupt Changes in Signal Processing.- The Computer, Music, and Sound Models.- III Wavelets and Signal Processing.- Wavelets and Seismic Interpretation.- Wavelet Transformations in Signal Detection.- Use of Wavelet Transforms in the Study of Propagation of Transient Acoustic Signals Across a Plane Interface Between Two Homogeneous Media.- Time-Frequency Analysis of Signals Related to Scattering Problems in Acoustics Part I: Wigner-Ville Analysis of Echoes Scattered by a Spherical Shell.- Coherence and Projectors in Acoustics.- Wavelets and Granular Analysis of Speech.- Time-Frequency Representations of Broad-Band Signals.- Operator Groups and Ambiguity Functions in Signal Processing.- IV Mathematics and Mathematical Physics.- Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems.- Holomorphic Integral Representations for the Solutions of the Helmholtz Equation.- Wavelets and Path Integrals.- Mean Value Theorems and Concentration Operators in Bargmann and Bergman Space.- Besov-Sobolev Algebras of Symbols.- Poincare Coherent States and Relativistic Phase Space Analysis.- A Relativistic Wigner Function Affiliated with the Weyl-Poincare Group.- Wavelet Transforms Associated to the n-Dimensional Euclidean Group with Dilations: Signal in More Than One Dimension.- Construction of Wavelets on Open Sets.- Wavelets on Chord-Arc Curves.- Multiresolution Analysis in Non-Homogeneous Media.- About Wavelets and Elliptic Operators.- Towards a Method for Solving Partial Differential Equations Using Wavelet Bases.- V Implementations.- A Real-Time Algorithm for Signal Analysis with the Help of the Wavelet Transform.- An Implementation of the "algorithme a trous" to Compute the Wavelet Transform.- An Algorithm for Fast Imaging of Wavelet Transforms.- Multiresolution Approach to Wavelets in Computer Vision.- Index of Contributors.
70 citations
TL;DR: The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real.
Abstract: The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real. An algorithm for taking the Hartley transform of a long sequence on a multiprocessor machine by simultaneously transforming short subsequences does not require complex arithmetic and is faster than analogous techniques which use the Fourier transform.
9 citations
14 Nov 1989
TL;DR: It is shown that Zak transform is a major tool in analysis and synthesis of non-stationary signals.
Abstract: A Zak transform is defined which plays a role in wavelet analysis based on the affine group completely analogous to the role played by the Zak transform on the wavelet analysis based on the Weyl-Heisenberg group. It is shown that Zak transform is a major tool in analysis and synthesis of non-stationary signals.
4 citations
TL;DR: In this article, a hybrid method that combines a Laplace transform technique with a direct integration scheme is presented, which results in accuracies unattainable with direct integration alone at only a small additional computational cost.
TL;DR: The bit-reversal operation for scrambling and coefficient determination within fast Fourier transform algorithms and how they can be accelerated with TMS32010-based processors are discussed.