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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Enveloped Sinusoid Parseval Frames
TL;DR: Numerical experiments on acoustics data reveal that the accessibility of this method allows it to be simultaneously competitive with the STFT in time-frequency processing and also with Prony’s Method for time-constant parameter estimation, surpassing the shortcomings of each individual technique.
Journal ArticleDOI
A Novel Fault Diagnosis Approach for Rolling Bearing Based on CWT and Adaptive Sparse Representation
X. Yuan,Huijie Zhang,Hui Li +2 more
TL;DR: An adaptive sparse representation (ASR) method is proposed, which integrates the sparse code shrinkage (SCS) and parameter optimization into TQWT and the results of simulated and experimental vibration signal analyses verify the effectiveness of the proposed method in accurately extracting weak impulse features from the noise environment.
Proceedings ArticleDOI
Research on classification of motor imagery EEG signals based on TQWT-CSP
Jianfeng Jia,Rui Zhang +1 more
TL;DR: In this paper , a feature extraction method called TQWT-CSP based on sliding time window is proposed, which can extract the spatial features of multiple time-frequency blocks, so as to select different optimal feature sets for different individuals before motor imagery classification is completed.
Journal ArticleDOI
A novel PRFB decomposition for non-stationary time-series and image analysis
TL;DR: In this paper , the authors proposed a novel perfect reconstruction filterbank decomposition (PRFBD) method for nonlinear and non-stationary time-series and image data representation and analysis.
Journal ArticleDOI
Optimized Tunable-Q Wavelet Transform Based 2D ECG Compression Technique Using DCT
TL;DR: In this paper , a novel compression algorithm by combining discrete cosine transform (DCT) and optimized tunable-Q wavelet transform (TQWT) for compression of 2D ECG signals is presented.
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.
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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.
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.