Journal ArticleDOI
Algorithm 735: Wavelet transform algorithms for finite-duration discrete-time signals
Carl Taswell,Kevin C. McGill +1 more
TLDR
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 brieflyread more
Citations
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Book
Wavelet Methods for Time Series Analysis
TL;DR: Wavelet analysis of finite energy signals and random variables and stochastic processes, analysis and synthesis of long memory processes, and the wavelet variance.
Book ChapterDOI
The Stationary Wavelet Transform and some Statistical Applications
TL;DR: In this article, two different approaches to the construction of an inverse of the stationary wavelet transform are described, and a method of local spectral density estimation is developed, which involves extensions to the wavelet context of standard time series ideas such as the periodogram and spectrum.
Journal ArticleDOI
Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding
Arne Kovac,Bernard W. Silverman +1 more
TL;DR: In this paper, the authors proposed a variance calculation algorithm for nonparametric regression with wavelet expansion, which allows data on any set of independent variable values to be treated, by first interpolating to a fine regular grid of suitable length, and then constructing a wavelet expand of the gridded data.
Proceedings ArticleDOI
Matthan: Drone Presence Detection by Identifying Physical Signatures in the Drone's RF Communication
TL;DR: It is examined whether physical characteristics of the drone, such as body vibration and body shifting, can be detected in the wireless signal transmitted by drones during communication and whether the received drone signals are uniquely differentiated from other mobile wireless phenomena such as cars equipped with Wi- Fi or humans carrying a mobile phone.
Book ChapterDOI
Choice of the Threshold Parameter in Wavelet Function Estimation
TL;DR: This work describes how it has applied the statistical technique of cross-validation to choose a threshold and presents results that indicate that its performance for correlated data.
References
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Journal ArticleDOI
A theory for multiresolution signal decomposition: the wavelet representation
TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
Journal ArticleDOI
Orthonormal bases of compactly supported wavelets
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
Journal ArticleDOI
The Laplacian Pyramid as a Compact Image Code
Peter J. Burt,Edward H. Adelson +1 more
TL;DR: A technique for image encoding in which local operators of many scales but identical shape serve as the basis functions, which tends to enhance salient image features and is well suited for many image analysis tasks as well as for image compression.
Journal ArticleDOI
Wavelets and signal processing
Olivier Rioul,Martin Vetterli +1 more
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.
Journal ArticleDOI
Continuous and discrete wavelet transforms
Christopher Heil,David F. Walnut +1 more
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.