The wavelet transform and time-varying tiling of the time-frequency plane

Author(s):  
K. Nayebi ◽  
I. Sodagar ◽  
T.P. Barnwell
Author(s):  
Jean Baptiste Tary ◽  
Roberto Henry Herrera ◽  
Mirko van der Baan

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution. Yet, interpretation of the resulting spectral decomposition is often hindered by smearing and leakage of individual frequency components. Computation of instantaneous frequencies, combined by frequency reassignment, may then be applied by highly localized techniques, such as the synchrosqueezing transform and ConceFT, in order to reduce these effects. In this paper, we present the synchrosqueezing transform together with the CWT and illustrate their relative performances using four signals from different fields, namely the LIGO signal showing gravitational waves, a ‘FanQuake’ signal displaying observed vibrations during an American football game, a seismic recording of the M w 8.2 Chiapas earthquake, Mexico, of 8 September 2017, followed by the Irma hurricane, and a volcano-seismic signal recorded at the Popocatépetl volcano showing a tremor followed by harmonic resonances. These examples illustrate how high-localization techniques improve analysis of the time-frequency information of time-varying signals. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.


2011 ◽  
Vol 54 (2) ◽  
pp. 85-102
Author(s):  
David Smallwood

A modified harmonic wavelet transform is used to estimate a time varying spectral density. The resolution of the estimate has an approximate constant time-frequency product. The estimation error is directly related to this time-frequency product. Unwanted cross product terms are effectively minimized. Several examples are given: White random, two sine waves, chirps, impulses, sums of exponentially decaying sinusoids, and a pyroshock. It is also shown how realizations can be generated from the modified harmonic wavelet transform estimate of the time varying spectral density.


2021 ◽  
Vol 11 (2) ◽  
pp. 752
Author(s):  
Gary W. Chang ◽  
Yu-Luh Lin ◽  
Yu-Jen Liu ◽  
Gary H. Sun ◽  
Johnson T. Yu

With widespread non-linear loads and the increasing penetration of distributed generations in the power system, harmonic pollution has become a great concern. The causes of harmonic pollution not only include the integer harmonics, but also interharmonics, which exacerbate the complexity of harmonic analysis. In addition, the output variability of highly non-linear loads and renewables such as electric arc furnaces and photovoltaic solar or wind generation may lead to weakly time-varying harmonics and interharmonics in both frequency and magnitude. These features present challenges for accurate assessment of associated power-quality (PQ) disturbances. To tackle such increasing time-varying PQ problems, a hybrid detection method using synchrosqueezing wavelet transform (SSWT) is proposed. The proposed method first obtains the proper parameter values for the mother wavelet according to numerical computations. The wavelet transform-based synchrosqueezing and a clustering method are applied to determine each frequency component of the waveform under assessment. The time-domain waveform and the associated magnitude of each frequency component is then reconstructed by the inverse SSWT operation. The novelty of the proposed method is that it can decompose the measured waveform containing both harmonics and interharmonics into intrinsic mode functions without the need for fundamental frequency detection. Compared to other time–frequency analysis methods, SSWT has better anti-noise and higher resolution of time–frequency curves; even the measured signal has close frequency components. Simulation results and actual measurement validations show that the proposed method is effective and relatively accurate in time-varying harmonic and interharmonic detection and is suitable for applications in power networks and microgrids that have high penetration of renewables or non-linear loads causing time-varying voltage or current waveforms.


1997 ◽  
Vol 117 (3) ◽  
pp. 338-345 ◽  
Author(s):  
Masatake Kawada ◽  
Masakazu Wada ◽  
Zen-Ichiro Kawasaki ◽  
Kenji Matsu-ura ◽  
Makoto Kawasaki

Author(s):  
Aarushi Shrivastava ◽  
Janki Ballabh Sharma ◽  
Sunil Dutt Purohit

Objective: In the recent multimedia technology images play an integral role in communication. Here in this paper, we propose a new color image encryption method using FWT (Fractional Wavelet transform), double random phases and Arnold transform in HSV color domain. Methods: Firstly the image is changed into the HSV domain and the encoding is done using the FWT which is the combination of the fractional Fourier transform with wavelet transform and the two random phase masks are used in the double random phase encoding. In this one inverse DWT is taken at the end in order to obtain the encrypted image. To scramble the matrices the Arnold transform is used with different iterative values. The fractional order of FRFT, the wavelet family and the iterative numbers of Arnold transform are used as various secret keys in order to enhance the level of security of the proposed method. Results: The performance of the scheme is analyzed through its PSNR and SSIM values, key space, entropy, statistical analysis which demonstrates its effectiveness and feasibility of the proposed technique. Stimulation result verifies its robustness in comparison to nearby schemes. Conclusion: This method develops the better security, enlarged and sensitive key space with improved PSNR and SSIM. FWT reflecting time frequency information adds on to its flexibility with additional variables and making it more suitable for secure transmission.


Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 119
Author(s):  
Tao Wang ◽  
Changhua Lu ◽  
Yining Sun ◽  
Mei Yang ◽  
Chun Liu ◽  
...  

Early detection of arrhythmia and effective treatment can prevent deaths caused by cardiovascular disease (CVD). In clinical practice, the diagnosis is made by checking the electrocardiogram (ECG) beat-by-beat, but this is usually time-consuming and laborious. In the paper, we propose an automatic ECG classification method based on Continuous Wavelet Transform (CWT) and Convolutional Neural Network (CNN). CWT is used to decompose ECG signals to obtain different time-frequency components, and CNN is used to extract features from the 2D-scalogram composed of the above time-frequency components. Considering the surrounding R peak interval (also called RR interval) is also useful for the diagnosis of arrhythmia, four RR interval features are extracted and combined with the CNN features to input into a fully connected layer for ECG classification. By testing in the MIT-BIH arrhythmia database, our method achieves an overall performance of 70.75%, 67.47%, 68.76%, and 98.74% for positive predictive value, sensitivity, F1-score, and accuracy, respectively. Compared with existing methods, the overall F1-score of our method is increased by 4.75~16.85%. Because our method is simple and highly accurate, it can potentially be used as a clinical auxiliary diagnostic tool.


2013 ◽  
Vol 333-335 ◽  
pp. 650-655
Author(s):  
Peng Hui Niu ◽  
Yin Lei Qin ◽  
Shun Ping Qu ◽  
Yang Lou

A new signal processing method for phase difference estimation was proposed based on time-varying signal model, whose frequency, amplitude and phase are time-varying. And then be applied Coriolis mass flowmeter signal. First, a bandpass filtering FIR filter was applied to filter the sensor output signal in order to improve SNR. Then, the signal frequency could be calculated based on short-time frequency estimation. Finally, by short window intercepting, the DTFT algorithm with negative frequency contribution was introduced to calculate the real-time phase difference between two enhanced signals. With the frequency and the phase difference obtained, the time interval of two signals was calculated. Simulation results show that the algorithms studied are efficient. Furthermore, the computation of algorithms studied is simple so that it can be applied to real-time signal processing for Coriolis mass flowmeter.


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