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
Weak fault feature extraction of rolling element bearings based on ensemble tunable Q-factor wavelet transform and non-dominated negentropy
TL;DR: In this paper , a novel method based on ensemble TQWT and non-dominated negentropy is proposed for weak repetitive transient extraction of rolling element bearings, where the vibration signal is decomposed with couples of Q-factors and redundancies.
Proceedings ArticleDOI
Enveloped Sinusoid Parseval Frames
TL;DR: In this paper , the Enveloped Sinusoid Parseval (ESP) frames can represent a wide variety of signal types as specified by their physical morphology, which is compatible with large scale and iterative optimization algorithms.
Proceedings ArticleDOI
A method to separate flexural and extensional signals from mixed-mode ultrasonic signals
Jean-Luc Le Calvez,T. M. Brill +1 more
TL;DR: In this article, a new technique was proposed to separate the mixed single-mode signals in ultrasonic transducers with a frequency-thickness product in the range of 1 to 3 MHz·mm.
Journal ArticleDOI
Magnetic Anomaly Feature Extraction Using the Tunable Q-factor Wavelet Transform Based on Non-convex Overlapping Group Shrinkage
TL;DR: In this article, a sparse feature extraction method based on the tunable Q-factor wavelet transform and overlapping group shrinkage is developed to extract weak features from signals with group property.
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.