Localization operators, time frequency concentration and quantitative-type uncertainty for the continuous wavelet transform associated with spherical mean operator

2019 ◽  
Vol 17 (04) ◽  
pp. 1950022 ◽  
Author(s):  
Hatem Mejjaoli ◽  
Nadia Ben Hamadi ◽  
Slim Omri
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Finite Measure ◽  
Continuous Wavelet ◽  
Uncertainty Principles ◽  
Localization Operators ◽  
Spherical Mean Operator ◽  
Von Neumann ◽  
Time Frequency ◽  
Spherical Mean

We consider the continuous wavelet transform [Formula: see text] associated with the spherical mean operator. We investigate the localization operators for [Formula: see text], in particular, we prove that they are in the Schatten-von Neumann class. Next, we analyze the concentration of this transform on sets of finite measure. In particular, Donoho-Stark and Benedicks-type uncertainty principles are given. Finally, we prove many versions of quantitative uncertainty principles for [Formula: see text].

Localization operators of the wavelet transform associated to the Riemann–Liouville operator

2016 ◽  
Vol 27 (04) ◽  
pp. 1650036 ◽  
Author(s):  
C. Baccar ◽  
N. B. Hamadi
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Liouville Operator ◽  
Continuous Wavelet ◽  
Localization Operators ◽  
Von Neumann ◽  
Neumann Class

We study the continuous wavelet transform [Formula: see text] associated with the Riemann–Liouville operator. Next, we investigate the localization operators for [Formula: see text]; in particular we prove that they are in the Schatten-von Neumann class.

scholarly journals Automatic ECG Classification Using Continuous Wavelet Transform and Convolutional Neural Network

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 119
Author(s):  
Tao Wang ◽  
Changhua Lu ◽  
Yining Sun ◽  
Mei Yang ◽  
Chun Liu ◽  
...  
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Convolutional Neural Network ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Ecg Signals ◽  
Rr Interval ◽  
Frequency Components ◽  
Fully Connected

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.

scholarly journals Ground Penetrating Radar for Belowground Phenotyping of High-biomass Grasses for Soil Carbon Sequestration

2021 ◽  
Author(s):  
Matthew Wolfe ◽  
Da Huo ◽  
Henry Ruiz-Guzman ◽  
Brody Teare ◽  
Tyler Adams ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Carbon Capture ◽  
Large Scale ◽  
Agricultural Practices ◽  
Signal Amplitude ◽  
Belowground Biomass ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Non Invasive

Abstract AimsMany governments and companies have committed to moving to net-zero emissions by 2030 or 2050 to tackle climate change, which require the development of new carbon capture and sequestration/storage (CCS) techniques. A proposed method of sequestration is to deposit carbon in soils as plant matter including root mass and root exudates. Adding perennial traits such as rhizomes to crops as part of a sequestration strategy would result in annual crop regrowth from rhizome meristems rather than requiring replanting from seeds which would in turn encourage no-till agricultural practices. Integrating these traits into productive agriculture requires a belowground phenotyping method compatible with high throughput breeding and selection methods (i.e., is rapid, inexpensive, reliable, and non-invasive), however none currently exist. MethodsGround penetrating radar (GPR) is a non-invasive subsurface sensing technology that shows potential as a phenotyping technique. In this study, a prototype GPR antenna array was used to scan roots of the perennial sorghum hybrid, PSH09TX15. A-scan level time-domain analyses and B-scan level time/frequency analyses using the continuous wavelet transform were utilized to extract features of interest from the acquired radargrams. ResultsOf six A-scan diagnostic indices examined, the standard deviation of signal amplitude correlated most significantly with belowground biomass. Time frequency analysis using the continuous wavelet transform yielded high correlations of B-scan features with belowground biomass. ConclusionThese results demonstrate that continued refinement of GPR data analysis workflows should yield a highly applicable phenotyping tool for breeding efforts in environments where selection is otherwise impractical on a large scale.

scholarly journals Application of Continuous Wavelet Transform and Convolutional Neural Network in Decoding Motor Imagery Brain-Computer Interface

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1199 ◽  
Author(s):  
Hyeon Kyu Lee ◽  
Young-Seok Choi
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Convolutional Neural Network ◽  
Motor Imagery ◽  
Continuous Wavelet Transform ◽  
Brain Computer Interface ◽  
Classification Performance ◽  
Computer Interface ◽  
Continuous Wavelet ◽  
Time Frequency

The motor imagery-based brain-computer interface (BCI) using electroencephalography (EEG) has been receiving attention from neural engineering researchers and is being applied to various rehabilitation applications. However, the performance degradation caused by motor imagery EEG with very low single-to-noise ratio faces several application issues with the use of a BCI system. In this paper, we propose a novel motor imagery classification scheme based on the continuous wavelet transform and the convolutional neural network. Continuous wavelet transform with three mother wavelets is used to capture a highly informative EEG image by combining time-frequency and electrode location. A convolutional neural network is then designed to both classify motor imagery tasks and reduce computation complexity. The proposed method was validated using two public BCI datasets, BCI competition IV dataset 2b and BCI competition II dataset III. The proposed methods were found to achieve improved classification performance compared with the existing methods, thus showcasing the feasibility of motor imagery BCI.

scholarly journals Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170254 ◽  
Author(s):  
Jean Baptiste Tary ◽  
Roberto Henry Herrera ◽  
Mirko van der Baan
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Seismic Signal ◽  
American Football ◽  
Frequency Resolution ◽  
Time Varying ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Frequency Information ◽  
Synchrosqueezing Transform

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’.

scholarly journals Time-frequency analysis of the Surge Onset in the Centrifugal Blower

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Grzegorz Liskiewicz ◽  
Longin Horodko
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Working Condition ◽  
Continuous Wavelet ◽  
Transient Phase ◽  
Centrifugal Blower ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Pressure Signal

Abstract Time frequency analysis of the surge onset was performed in the centrifugal blower. A pressure signal was registered at the blower inlet, outlet and three locations at the impeller shroud. The time-frequency scalograms were obtained by means of the Continuous Wavelet Transform (CWT). The blower was found to successively operate in four different conditions: stable working condition, inlet recirculation, transient phase and deep surge. Scalograms revealed different spectral structures of aforementioned phases and suggest possible ways of detecting the surge predecessors.

Spectral decomposition of seismic data with continuous-wavelet transform

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. P19-P25 ◽  
Author(s):  
Satish Sinha ◽  
Partha S. Routh ◽  
Phil D. Anno ◽  
John P. Castagna
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Scale ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Map

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

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