Journal ArticleDOI
Wavelet Transform With Tunable Q-Factor
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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.read more
Citations
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Journal ArticleDOI
PrimePatNet87: Prime pattern and tunable q-factor wavelet transform techniques for automated accurate EEG emotion recognition.
Abdullah Dogan,Merve Akay,Prabal Datta Barua,Prabal Datta Barua,Mehmet Baygin,Sengul Dogan,Turker Tuncer,Ali H. Dogru,U. Rajendra Acharya,U. Rajendra Acharya,U. Rajendra Acharya +10 more
TL;DR: In this article, a novel prime pattern and tunable q-factor wavelet transform (TQWT) techniques were used to classify human emotions using electroencephalogram (EEG) signals.
Journal ArticleDOI
Intelligent bearing fault signature extraction via iterative oscillatory behavior based signal decomposition (IOBSD)
Juanjuan Shi,Ming Liang +1 more
TL;DR: The main features of the proposed OBSD method include: it can remove in-band interference and noise that cannot be removed by the widely used frequency-based approaches, as it is frequency-independent in nature, it can extract fault signatures from heavily interference-obscured signals without filtering the signals, and it does not require the prior information of the signals.
Journal ArticleDOI
Intelligent fault diagnosis of rolling element bearings using sparse wavelet energy based on overcomplete DWT and basis pursuit
Cong Wang,Meng Gan,Chang’an Zhu +2 more
TL;DR: SWE features that combine the merits of overcomplete DWT and sparse representation techniques can precisely reveal fault-induced information, thereby exhibiting valuable properties for automatic fault identification by intelligent classifiers.
Journal ArticleDOI
A method for tachometer-free and resampling-free bearing fault diagnostics under time-varying speed conditions
TL;DR: A new tachometer-free and resampling-free method is proposed for bearing fault diagnosis under time-varying speed conditions which consists of three main steps: bearing fault signature extraction via Oscillatory Behavior-based Signal Decomposition (OBSD) to suppress the influence of random noise and interferences, and automatic bearing fault identification based on the average curve-to-curve ratios of the searched IFCF and ISRF.
Journal ArticleDOI
Gear Fault Diagnosis Based on Dual Parameter Optimized Resonance-Based Sparse Signal Decomposition of Motor Current
TL;DR: In this article, the dual parameters optimized resonance-based sparse signal decomposition (RSSD) method was proposed to extract fault features from these interferences, which can decompose a complex signal into a high- and low-resonance component with two sets of overcomplete wavelet bases.
References
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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.
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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.
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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.