Multiresolution approximations and wavelet orthonormal bases of L^2(R)
TLDR
In this paper, the authors study the properties of multiresolution approximation and prove that it is characterized by a 2π periodic function, which is further described in terms of wavelet orthonormal bases.Abstract:
A multiresolution approximation is a sequence of embedded vector spaces V j jmember Z for approximating L 2 (R) functions. We study the properties of a multiresolution approximation and prove that it is characterized by a 2π periodic function which is further described. From any multiresolution approximation, we can derive a function ψ(x) called a wavelet such that √ 2 j ψ(2 j x −k) (k ,j)member Z 2 is an orthonormal basis of L 2 (R). This provides a new approach for understanding and computing wavelet orthonormal bases. Finally, we characterize the asymptotic decay rate of multiresolution approximation errors for functions in a Sobolev space H s .read more
Citations
More filters
Proceedings ArticleDOI
Multi-scale wavelet modulation
TL;DR: The purpose of this paper is to provide the fundamental characterization of a general multidimensional modulation format which utilizes wavelet basis functions as pulse shapes and an efficient digital implementation utilizing digital filter banks is put forth.
Journal ArticleDOI
Quasi-Biorthogonal Frame Multiresolution Analyses and Wavelets
TL;DR: The concepts of quasi-biorthogonal frame multiresolution analyses and quasi- biorthogsonal frame wavelets are introduced which are natural generalizations of biorstogonal multiresolved analyses and biorTHogonal wavelets, respectively.
Journal ArticleDOI
Wavelet decomposition method decoupled boiling/evaporation oscillation mechanisms over two to three timescales: A study for a microchannel with pin fin structure
TL;DR: In this paper, the wavelet decomposition method was used to identify the noise signal and decoupled various temperature oscillations with different amplitudes and frequencies in a microchannel with pin fin structure.
Journal ArticleDOI
Ultrasonic Detection Method for Grouted Defects in Grouted Splice Sleeve Connector Based on Wavelet Pack Energy.
TL;DR: A wavelet packet analysis algorithm was developed to effectively detect grouted defects using the ultrasonic method, and a verified experiment demonstrated that when thegrouted defects reached certain sizes, the proposed method could detect the grouting defects effectively.
Journal ArticleDOI
Forecasting Network Traffic Load Using Wavelet Filters and Seasonal Autoregressive Moving Average Model
TL;DR: This paper uses the wavelet filters based on multi-resolution analysis along with the Seasonal Autoregressive Moving Average (SARIMA) models for forecasting network traffic volume and concludes that the proposed method give better and accurate forecasts.
References
More filters
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
Decomposition of Hardy functions into square integrable wavelets of constant shape
A. Grossmann,J. Morlet +1 more
TL;DR: In this article, the authors studied square integrable coefficients of an irreducible representation of the non-unimodular $ax + b$-group and obtained explicit expressions in the case of a particular analyzing family that plays a role analogous to coherent states (Gabor wavelets) in the usual $L_2 $ -theory.
Journal ArticleDOI
Exact reconstruction techniques for tree-structured subband coders
TL;DR: It is shown that it is possible to design tree-structured analysis/reconstruction systems which meet the sampling rate condition and which result in exact reconstruction of the input signal.
Journal ArticleDOI
Analysis of sound patterns through wavelet transforms
TL;DR: The main features of so-called wavelet transforms are illustrated through simple mathematical examples and the first applications of the method to the recognition and visualisation of characteristic features of speech and of musical sounds are presented.