Efficient Algorithms for Discrete Wavelet Transform
01 Jan 2013-
TL;DR: This book focuses on and around new implementation techniques of discrete wavelet transform (DWT) and their applications in denoising and classification and their impact on signal processing theory and practice.
Abstract: Wavelet transforms (WT) have growing impact on signal processing theory and practice. This is because of two reasons: (a) unifying role of wavelet transform and (b) their successes in wide variety of applications. Digital filter banks, the basis of wavelet-based algorithms, have become standard signal processing operators. Filter banks are the fundamental tools required for processing of real signals using digital signal processors (DSP) [133,139]. Vaidyanathan in his book [134] has discussed connection between theory of filter bank and DSP. The purpose of this book is to look at wavelet-related issues from a signal processing perspective. This book focuses on and around new implementation techniques of discrete wavelet transform (DWT) and their applications in denoising and classification. On this account, it is required to introduce the wavelet theory in brief. The organization of this chapter is as follows: Section 1.1 introduces the subject in brief. Section 1.2 presents historical review of multiresolution analysis and wavelet transform. Various kinds of wavelet transform applied to signal processing applications viz. continuous wavelet transform (CWT) and DWT (one dimension and two dimensions) are discussed in brief. Section 1.3 reviews implementation issues and applications of DWT from signal processing viewpoint. Section 1.4 concludes this chapter by outlining major contribution of the book.
Citations
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TL;DR: In this paper, a multi-scale proper orthogonal decomposition (mPOD) is proposed, which combines multi-resolution analysis (MRA) with a standard POD.
Abstract: Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.
90 citations
TL;DR: In this paper, a novel approach for detecting and classifying faults in power systems is called maximum wavelet singular value (MWSV), which is based on the discrete wavelet transform (DWT) and singular value decomposition (SVD).
Abstract: In this study, a novel algorithm for detecting and classifying faults in high-voltage transmission lines is proposed. The algorithm is based on the discrete wavelet transform (DWT) and singular value decomposition (SVD). The DWT is used for extracting the currents’ high-frequency components under fault conditions. Signals under each fault condition are scaled in frequency, in order to build a wavelet matrix. By means of the SVD, the maximum singular value is calculated and employed in this proposal. The attained results exhibit that the maximum singular value represents a good indicator for the issue. This novel approach for detecting and classifying faults in power systems is called maximum wavelet singular value. Phase-to-ground, two-phase to ground, and three-phase faults’ simulations under different fault impedances are carried out by DIgSILENT Power Factory. The analysed fault conditions are evaluated demonstrating that the proposal reduces the computational burden and the time detection.
69 citations
Journal Article•
TL;DR: The wavelet transform is an analytical method which units the time domain and frequency domain and is called a methematical microscope for analyzing signals.
Abstract: Wavelet transform is an analytical method which units the time domain and frequency domain. It has 3 features: (1) Multiresolution; (2) Constant relative bandwidth; (3) Wavelets has the ability to indicate signals which is localized in time or space. It is called a methematical microscope for analyzing signals. The Windows operating system is used as the platform, the EEG signal is analyzed with the wavelet transform in the EEG process system. This system accomplishes some functions such as case history manahement, EEG signal at the rate of 100Hz, EEG data store for 10 minutes. It is an EEG signal analytical system.
37 citations
TL;DR: The proposed scheme for a multi-terminal transmission line protection scheme based on wavelet packet transform is efficient and shows high speed and accuracy of fault detection compared to other methods in the literature.
36 citations
Cites background from "Efficient Algorithms for Discrete W..."
...The complexity of the WPT is as shown in the following equation (12): (12) where S is the length of signal, L is the filter length, and n is the level of decomposition [58]....
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05 Jun 2016
TL;DR: This paper presents an effective method based on wavelet transform and support vector machines (SVM) for detection of arc faults in DC PV systems that is compared with traditional Fourier transform based approaches.
Abstract: Arc faults pose significant reliability and safety issues in today's photovoltaic (PV) systems. This paper presents an effective method based on wavelet transform and support vector machines (SVM) for detection of arc faults in DC PV systems. Because of its advantages in time-frequency signal processing, wavelet transform is applied to extract the characteristic features from system voltage/current signals. SVM is then used to identify arc faults. The performance of the proposed technique is compared with traditional Fourier transform based approaches.
30 citations
References
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TL;DR: Although the new index is mathematically defined and no human visual system model is explicitly employed, experiments on various image distortion types indicate that it performs significantly better than the widely used distortion metric mean squared error.
Abstract: We propose a new universal objective image quality index, which is easy to calculate and applicable to various image processing applications. Instead of using traditional error summation methods, the proposed index is designed by modeling any image distortion as a combination of three factors: loss of correlation, luminance distortion, and contrast distortion. Although the new index is mathematically defined and no human visual system model is explicitly employed, our experiments on various image distortion types indicate that it performs significantly better than the widely used distortion metric mean squared error. Demonstrative images and an efficient MATLAB implementation of the algorithm are available online at http://anchovy.ece.utexas.edu//spl sim/zwang/research/quality_index/demo.html.
5,285 citations
Book•
01 Jul 1992
TL;DR: In this paper, a review of Discrete-Time Multi-Input Multi-Output (DIMO) and Linear Phase Perfect Reconstruction (QLP) QMF banks is presented.
Abstract: 1. Introduction 2. Review of Discrete-Time Systems 3. Review of Digital Filters 4. Fundamentals of Multirate Systems 5. Maximally Decimated Filter Banks 6. Paraunitary Perfect Reconstruction Filter Banks 7. Linear Phase Perfect Reconstruction QMF Banks 8. Cosine Modulated Filter Banks 9. Finite Word Length Effects 10. Multirate Filter Bank Theory and Related Topics 11. The Wavelet Transform and Relation to Multirate Filter Banks 12. Multidimensional Multirate Systems 13. Review of Discrete-Time Multi-Input Multi-Output LTI Systems 14. Paraunitary and Lossless Systems Appendices Bibliography Index
4,757 citations
Book•
11 Aug 2011TL;DR: The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges and shows that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures.
Abstract: A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. They show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below visual sensitivity. As an application, a compact image coding algorithm that selects important edges and compresses the image data by factors over 30 has been implemented. >
3,187 citations
CNET1
TL;DR: A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes, which includes nonstationary signal analysis, scale versus frequency,Wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing.
Abstract: A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes. The discussion includes nonstationary signal analysis, scale versus frequency, wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing. The main definitions and properties of wavelet transforms are covered, and connections among the various fields where results have been developed are shown. >
2,945 citations