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.

Time-frequency representation of digital signals and systems based on short-time Fourier analysis

Abstract: This paper develops a representation for discrete-time signals and systems based on short-time Fourier analysis. The short-time Fourier transform and the time-varying frequency response are reviewed as representations for signals and linear time-varying systems. The problems of representing a signal by its short-time Fourier transform and synthesizing a signal from its transform are considered. A new synthesis equation is introduced that is sufficiently general to describe apparently different synthesis methods reported in the literature. It is shown that a class of linear-filtering problems can be represented as the product of the time-varying frequency response of the filter multiplied by the short-time Fourier transform of the input signal. The representation of a signal by samples of its short-time Fourier transform is applied to the linear filtering problem. This representation is of practical significance because there exists a computationally efficient algorithm for implementing such systems. Finally, the methods of fast convolution age considered as special cases of this representation.

The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

Abstract: PREFACE GETTING STARTED THE CONTINUOUS WAVELET TRANSFORM Introduction The Wavelet Requirements for the Wavelet The Energy Spectrum of the Wavelet The Wavelet Transform Identification of Coherent Structures Edge Detection The Inverse Wavelet Transform The Signal Energy: Wavelet-Based Energy and Power Spectra The Wavelet Transform in Terms of the Fourier Transform Complex Wavelets: The Morlet Wavelet The Wavelet Transform, Short Time Fourier Transform and Heisenberg Boxes Adaptive Transforms: Matching Pursuits Wavelets in Two or More Dimensions The CWT: Computation, Boundary Effects and Viewing Endnotes THE DISCRETE WAVELET TRANSFORM Introduction Frames and Orthogonal Wavelet Bases Discrete Input Signals of Finite Length Everything Discrete Daubechies Wavelets Translation Invariance Biorthogonal Wavelets Two-Dimensional Wavelet Transforms Adaptive Transforms: Wavelet Packets Endnotes FLUIDS Introduction Statistical Measures Engineering Flows Geophysical Flows Other Applications in Fluids and Further Resources ENGINEERING TESTING, MONITORING AND CHARACTERISATION Introduction Machining Processes: Control, Chatter, Wear and Breakage Rotating Machinery Dynamics Chaos Non-Destructive Testing Surface Characterisation Other Applications in Engineering and Further Resources MEDICINE Introduction The Electrocardiogram Neuroelectric Waveforms Pathological Sounds, Ultrasounds and Vibrations Blood Flow and Blood Pressure Medical Imaging Other Applications in Medicine FRACTALS, FINANCE, GEOPHYSICS AND OTHER AREAS Introduction Fractals Finance Geophysics Other Areas APPENDIX: USEFUL BOOKS, PAPERS AND WEBSITES Useful Books and Papers Useful Websites REFERENCES INDEX

Multifocus Image Fusion and Restoration With Sparse Representation

Abstract: To obtain an image with every object in focus, we always need to fuse images taken from the same view point with different focal settings. Multiresolution transforms, such as pyramid decomposition and wavelet, are usually used to solve this problem. In this paper, a sparse representation-based multifocus image fusion method is proposed. In the method, first, the source image is represented with sparse coefficients using an overcomplete dictionary. Second, the coefficients are combined with the choose-max fusion rule. Finally, the fused image is reconstructed from the combined sparse coefficients and the dictionary. Furthermore, the proposed fusion scheme can simultaneously resolve the image restoration and fusion problem by changing the approximate criterion in the sparse representation algorithm. The proposed method is compared with spatial gradient (SG)-, morphological wavelet transform (MWT)-, discrete wavelet transform (DWT)-, stationary wavelet transform (SWT)-, curvelet transform (CVT)-, and nonsubsampling contourlet transform (NSCT)-based methods on several pairs of multifocus images. The experimental results demonstrate that the proposed approach performs better in both subjective and objective qualities.

Wavelets and electromagnetic power system transients

Abstract: The wavelet transform is introduced as a method for analyzing electromagnetic transients associated with power system faults and switching. This method, like the Fourier transform, provides information related to the frequency composition of a waveform, but it is more appropriate than the familiar Fourier methods for the nonperiodic, wide-band signals associated with electromagnetic transients. It appears that the frequency domain data produced by the wavelet transform may be useful for analyzing the sources of transients through manual or automated feature detection schemes. The basic principles of wavelet analysis are set forth, and examples showing the application of the wavelet transform to actual power system transients are presented.

Hypercomplex Fourier Transforms of Color Images

Abstract: Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed