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Journal ArticleDOI

Wavelet Transform With Tunable Q-Factor

Ivan Selesnick
- 01 Aug 2011 - 
- Vol. 59, Iss: 8, pp 3560-3575
TLDR
A discrete-time wavelet transform for which the Q-factor is easily specified and the transform can be tuned according to the oscillatory behavior of the signal to which it is applied, based on a real-valued scaling factor.
Abstract
This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of Z. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.

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Citations
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Journal ArticleDOI

Debonding Detection of Precast Concrete Segmental Bridges Using Ensemble Superwavelet Transform

TL;DR: An ensemble superwavelet transform (ESW) based on the combination of a tunable Q-factor wavelet transform and root-mean-square deviation is proposed, in which an integrated analysis method of structural damage identification and damage quantification is realized.
Journal ArticleDOI

Mental performance classification using fused multilevel feature generation with EEG signals

TL;DR: In this paper , an objective artificial intelligence model was proposed to quantify the clarity of thought during mental arithmetic tasks, which achieved an accuracy of 96.77% using O2 channel with a k-nearest neighbor classifier and reached 100.0% accuracy with the majority voting classifier.
Journal ArticleDOI

Cathode Position Detection in a Transferred Arc Plasma Using Artificial Neural Network

TL;DR: In this article , a machine learning technique is proposed to accurately detect the position of the cathode in a direct current (DC) transferred arc plasma system, where the measured voltage signal sampled at 20 kHz is processed using a tunable Q-factor wavelet transform (TQWT) followed by statistical features extraction and machine learning algorithm to provide accurate cathode position information.
Patent

Method and system for multi-talker babble noise reduction using q-factor based signal decomposition

TL;DR: In this paper, a system and method for improving intelligibility of speech is presented, which may include obtaining an input audio signal, decomposing the audio signal into a first component having low or no sustained oscillatory pattern, and a second component having high oscillatory patterns, further de-noising the second component based on data generated from the first component to obtained a modified second component, and outputting an audio signal having reduced noise, the output audio signal comprising the first components in combination with the modified second components.
References
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Book

Ten lectures on wavelets

TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI

Ten Lectures on Wavelets

TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
Journal ArticleDOI

Atomic Decomposition by Basis Pursuit

TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Journal ArticleDOI

Fast Image Recovery Using Variable Splitting and Constrained Optimization

TL;DR: A new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an l2 data-fidelity term and a nonsmooth regularizer is proposed.
Journal ArticleDOI

Calculation of a constant Q spectral transform

TL;DR: In this article, a constant Q transform with a constant ratio of center frequency to resolution has been proposed to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components.
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