Instantaneous spectral attributes using scales in continuous-wavelet transform

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA137-WA142 ◽  
Author(s):  
Satish Sinha ◽  
Partha Routh ◽  
Phil Anno
Keyword(s):  
Wavelet Transform ◽  
Frequency Spectrum ◽  
Continuous Wavelet Transform ◽  
Time Window ◽  
Frequency Resolution ◽  
Rock Properties ◽  
Center Frequency ◽  
Continuous Wavelet ◽  
Frequency Spectra ◽  
Time Frequency

Instantaneous spectral properties of seismic data — center frequency, root-mean-square frequency, bandwidth — often are extracted from time-frequency spectra to describe frequency-dependent rock properties. These attributes are derived using definitions from probability theory. A time-frequency spectrum can be obtained from approaches such as short-time Fourier transform (STFT) or time-frequency continuous-wavelet transform (TFCWT). TFCWT does not require preselecting a time window, which is essential in STFT. The TFCWT method converts a scalogram (i.e., time-scale map) obtained from the continuous-wavelet transform (CWT) into a time-frequency map. However, our method includes mathematical formulas that compute the instantaneous spectral attributes from the scalogram (similar to those computed from the TFCWT), avoiding conversion into a time-frequency spectrum. Computation does not require a predefined window length because it is based on the CWT. This technique optimally decomposes a multiscale signal. For nonstationary signal analysis, spectral decomposition from [Formula: see text] has better time-frequency resolution than STFT, so the instantaneous spectral attributes from CWT are expected to be better than those from STFT.

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’.

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.

The robustness of seismic attenuation measurements using fixed- and variable-window time-frequency transforms

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA123-WA135 ◽  
Author(s):  
Carl Reine ◽  
Mirko van der Baan ◽  
Roger Clark
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Window ◽  
Time Windows ◽  
Seismic Attenuation ◽  
Continuous Wavelet ◽  
Transmission Experiment ◽  
Time Frequency ◽  
S Transform ◽  
Variable Window

Frequency-based methods for measuring seismic attenuation are used commonly in exploration geophysics. To measure the spectrum of a nonstationary seismic signal, different methods are available, including transforms with time windows that are either fixed or systematically varying with the frequency being analyzed. We compare four time-frequency transforms and show that the choice of a fixed- or variable-window transform affects the robustness and accuracy of the resulting attenuation measurements. For fixed-window transforms, we use the short-time Fourier transform and Gabor transform. The S-transform and continuous wavelet transform are analyzed as the variable-length transforms. First we conduct a synthetic transmission experiment, and compare the frequency-dependent scattering attenuation to the theoretically predicted values. From this procedure, we find that variable-window transforms reduce the uncertainty and biasof the resulting attenuation estimate, specifically at the upper and lower ends of the signal bandwidth. Our second experiment measures attenuation from a zero-offset reflection synthetic using a linear regression of spectral ratios. Estimates for constant-[Formula: see text] attenuation obtained with the variable-window transforms depend less on the choice of regression bandwidth, resulting in a more precise attenuation estimate. These results are repeated in our analysis of surface seismic data, whereby we also find that the attenuation measurements made by variable-window transforms have a stronger match to their expected trend with offset. We conclude that time-frequency transforms with a systematically varying time window, such as the S-transform and continuous wavelet transform, allow for more robust estimates of seismic attenuation. Peaks and notches in the measured spectrum are reduced because the analyzed primary signal is better isolated from the coda, and because of high-frequency spectral smoothing implicit in the use of short-analysis windows.

Research on Partial Discharge De-Noising for Transformer Based on Synchro-Squeezed Continuous Wavelet Transform

2020 ◽  
Vol 19 (02) ◽  
pp. 2050021
Author(s):  
Yanchun Xu ◽  
Haiting Xia ◽  
Chao Tan ◽  
Zhenhua Li ◽  
Lu Mi
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Partial Discharge ◽  
High Rate ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Signal Distortion ◽  
Time Frequency ◽  
High Order Statistics ◽  
Resolution Single

Traditional time-frequency methods for partial discharge (PD) de-noising have some limitations such as low time-frequency resolution, single de-noising type and poor readability. In this paper, a novel de-noising algorithm based on synchro-squeezed continuous wavelet transform (CWT) is adopted to filter out narrowband noise and white noise. The synchro-squeezed CWT algorithm is designed to redistribute the time-frequency domain and to distinguish the signal from the noise carefully as a high-rate time-frequency analysis. High-order statistics is employed to pre-process the polluted PD signal. The generalized cross-validation (GCV) threshold is combined with the adaptive trimmed threshold of synchro-squeezing (SS) domain to deal with the subsequent signals. The proposed algorithm can effectively suppress two kinds of noise, and the signal distortion is lower.

Instantaneous frequency estimation and representation of the audio signal through Complex Wavelet Additive Synthesis

2014 ◽  
Vol 12 (03) ◽  
pp. 1450030 ◽  
Author(s):  
Jesús Ponce de León ◽  
José Ramón Beltrán ◽  
Fernando Beltrán
Keyword(s):  
Wavelet Transform ◽  
Comparative Study ◽  
Continuous Wavelet Transform ◽  
Instantaneous Frequency ◽  
Audio Signal ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Complex Wavelet ◽  
Additive Synthesis

In this work, an improvement of the Complex Wavelet Additive Synthesis (CWAS) algorithm is presented. This algorithm is based on a discrete version of the Complex Continuous Wavelet Transform (CCWT) which analyzes the input signal in a frame-to-frame approach and under variable frequency resolution per octave. After summarizing several Time-Frequency Distributions (TFD), concretely the standard Short Time Fourier Transform (STFT), the Pseudo Wigner–Ville Distribution (PWVD), reassignment and complex wavelets, a comparative study of the accuracy in the instantaneous frequency (IF) estimation is shown. The comparative study includes three different signal processing tools (based on the summarized TFD): the Time-Frequency Toolbox (TFTB) of François Auger, the High Resolution Spectrographic Routines (HRSR) of Sean Fulop and the proposed CWAS algorithm. A set of eight synthetic signals have been analyzed using six different methods: the regular STFT spectrogram, the PWVD, their corresponding reassigned versions, the Nelson crossed spectrum method and finally the Complex Continuous Wavelet Transform (CCWT). Finally, two- and three-dimensional Time-Frequency representations of the IF provided by the CWAS algorithm are presented.

scholarly journals Frequency bandwidth enhancement using continuous wavelet transform and random noise attenuation by f-xy filtering technique – a case study from Badin oilfield, Indus basin, Pakistan

2019 ◽  
Vol 133 ◽  
pp. 01007
Author(s):  
Asad Taimur ◽  
Akinniyi Akinsunmade ◽  
Sylwia Tomecka-Suchon ◽  
Fahad Mehmood
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Seismic Data ◽  
Random Noise ◽  
Resolving Power ◽  
Indus Basin ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Bandwidth Extension ◽  
Time Frequency

Routine seismic data processing does not always meet the quantitative interpreters’ expectations especially in areas like Badin, where prospective thin bed B – sand interval is ambiguous throughout the seismic volume. Continuous Wavelet Transform (CWT) provides detailed description of seismic signal in both time and frequency without compromising on window length and a fixed time-frequency resolution over time-frequency spectrum. We present enhancement of seismic data for effective interpretation using the bandwidth extension technique. Implementing bandwidth extension, the dominant frequency increases from 18 Hz to 30 Hz and the frequency content boosted from 40 Hz to 60 Hz. Noise inclusion by the technique was suppressed by F-XY predictive filter and F-XY deconvolution with edge preserve smoothing. Phase and spectral balancing were applied to partial angle stacks to stabilize the phase rotation across the 3D survey, particularly for far offset stack. Frequency was balanced using surface consistent spectrum balancing, and subjected to trace scaling for amplitudes balance and preservation. Results of the techniques yielded unique improvement on the data resolution and subtle information about the thin sand beds were better delineated. Tuning thickness analysis reveals the usefulness of bandwidth extension, with an increase of 30% in the resolving power of thin beds.

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.

Adaptive Multiple Second-order Synchrosqueezing Wavelet Transform and Its Application in Wind Turbine Gearbox Fault Diagnosis

2021 ◽  
Author(s):  
Zhaohong Yu ◽  
Cancan Yi ◽  
Xiangjun Chen ◽  
Tao Huang
Keyword(s):  
Wavelet Transform ◽  
Wind Turbine ◽  
Time Window ◽  
Vibration Signal ◽  
Second Order ◽  
Center Frequency ◽  
Wind Turbine Gearbox ◽  
Adaptive Wavelet ◽  
Time Frequency ◽  
Window Width

Abstract Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing Time-Frequency (TF) Analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated Time-Frequency Representation (TFR), this paper proposes a new TFA method, namely Adaptive Multiple Second-order Synchrosqueezing Wavelet Transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical Continuous Wavelet Transform (CWT), and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus Adaptive Wavelet Transform (AWT) is generated. Then, on the basis of the theoretical framework of Synchrosqueezing Transform (SST) and accurate Instantaneous Frequency (IF) estimation by the utilization of second-order local demodulation operator, Adaptive Second-order Synchrosqueezing Wavelet Transform (AWSST2) is formed. Considering that the quality of actual time-frequency analysis is greatly disturbed by noise components, through performing multiple Synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since Synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.

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.

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