Journal ArticleDOI
Wavelet Transform With Tunable Q-Factor
Reads0
Chats0
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
More filters
Journal ArticleDOI
Robust Fringe Projection Profilometry via Sparse Representation
Budianto,Daniel P. K. Lun +1 more
TL;DR: Experimental results show that the proposed algorithm can significantly improve the robustness of an FPP system and performs equally well no matter the fringe images have a simple or complex scene, or are affected due to the ambient lighting of the working environment.
Journal ArticleDOI
Fault detection and diagnosis of a wheelset-bearing system using a multi-Q-factor and multi-level tunable Q-factor wavelet transform
TL;DR: The results indicate that the MQML-TQWT effectively extracts WPIRs that may be associated with early faults in the wheelset-bearing system and is superior to the existing TQWT in extractingWPIRs.
Journal ArticleDOI
Auto-OBSD: Automatic parameter selection for reliable Oscillatory Behavior-based Signal Decomposition with an application to bearing fault signature extraction
TL;DR: In this article, a systematic approach to automatic selection of oscillatory behavior-based signal decomposition (OBSD) parameters for reliable extraction of bearing fault signatures is proposed. But, the quality of the result highly relies on the selection of method-related parameters.
Journal ArticleDOI
A recursive sparse representation strategy for bearing fault diagnosis
TL;DR: In this article, a recursive sparse representation (RSR) algorithm is proposed to solve the fault diagnosis of bearings from sparse representation in the time and frequency domains, where the tunable Q-factor wavelet transform (TQWT) filtering strategy is used to adaptively obtain the best wavelet with the signal vibration features.
Journal ArticleDOI
A recursive sparse representation strategy for bearing fault diagnosis
TL;DR: In this paper , a recursive sparse representation (RSR) algorithm is proposed to solve the fault diagnosis of bearings from sparse representation in the time and frequency domains, where the tunable Q-factor wavelet transform (TQWT) filtering strategy is used to adaptively obtain the best wavelet with the signal vibration features.
References
More filters
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.