Journal ArticleDOI
Wavelet Transform With Tunable Q-Factor
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
Compound fault diagnosis of rolling element bearings using multipoint sparsity–multipoint optimal minimum entropy deconvolution adjustment and adaptive resonance-based signal sparse decomposition:
TL;DR: The effectiveness of the proposed scheme is verified by its application to both simulated and experimental compound bearing fault vibration signals with strong interference, and its advantages are confirmed by comparisons of the results with those of an existing state-of theart method.
Journal ArticleDOI
Weighted sparsity-based denoising for extracting incipient fault in rolling bearing
TL;DR: Simulation and experimental results show that the proposed approach can successfully extract fault features from the signals of low signal to noise ratio, thus effectively improving computational efficiency.
Journal ArticleDOI
TQWT-assisted statistical process control method for condition monitoring and fault diagnosis of bearings in high-speed rail:
TL;DR: The proposed statistical condition monitoring and fault diagnosis method based on tunable Q-factor wavelet transform (TQWT) outperforms a traditional time-frequency method, the Wigner-Ville distribution method.
Journal ArticleDOI
A Time-Frequency Analysis Method for Low Frequency Oscillation Signals Using Resonance-Based Sparse Signal Decomposition and a Frequency Slice Wavelet Transform
Yan Zhao,Zhimin Li,Yonghui Nie +2 more
TL;DR: In this article, a time-frequency analysis method using resonance-based sparse signal decomposition (RSSD) and a frequency slice wavelet transform (FSWT) is proposed.
Journal ArticleDOI
Fault diagnosis of rolling element bearing compound faults based on sparse no-negative matrix factorization-support vector data description:
TL;DR: In this article, a fault diagnosis method of rolling element bearing compound faults based on Sparse No-Negative Matrix Factorization (SNMF)-Support Vector Data Description (SVDD) is proposed.
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.
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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.