A Review of Time-Frequency Analysis Techniques for Estimation of Group Velocities

1993 ◽  
Vol 64 (2) ◽  
pp. 157-167 ◽  
Author(s):  
Argun H. Kocaoglu ◽  
Leland T. Long
Keyword(s):  
Fourier Transform ◽  
Wigner Distribution ◽  
Spectral Estimation ◽  
Moving Window ◽  
Window Length ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Analysis Techniques ◽  
Short Time ◽  
Group Velocities

Abstract Time-frequency analysis techniques, including the classical use of zero crossings to measure period, have been widely used in seismology for the estimation of surface wave group velocities. Group velocity estimation by the short-time Fourier transform and the multiple filter techniques are equivalent. Although these techniques are used most often, their resolution is limited. The resolution is controlled by the window length in the short time Fourier transform and the filter band width in the multiple filter technique. The moving-window autoregressive spectral estimation provides the highest resolution with the shortest possible window length by predicting the properties of the signal outside the analysis window; however, high resolution is obtained at the expense of uncertainty in the amplitude. Recently, the Wigner distribution has been introduced as a tool for mapping dispersed surface waves into the time-frequency domain. Resolution of the Wigner distribution is comparable to that of the moving-window autoregressive spectral estimation. When the spectral density at a given time contains two or more dominant frequencies, their interference causes the Wigner distribution to introduce spurious spectral peaks complicating the interpretation. The Choi-Williams distribution, in which these interference effects are minimized, can be used for such dispersed signals. However, the implementation is computationally complex and the distribution offers only a medium resolution.

Constrained least-squares spectral analysis: Application to seismic data

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. V143-V167 ◽  
Author(s):  
Charles I. Puryear ◽  
Oleg N. Portniaguine ◽  
Carlos M. Cobos ◽  
John P. Castagna
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Seismic Data ◽  
Continuous Wavelet ◽  
Window Length ◽  
Short Time Fourier Transform ◽  
Constrained Least Squares ◽  
Time Frequency ◽  
Short Time

An inversion-based algorithm for computing the time-frequency analysis of reflection seismograms using constrained least-squares spectral analysis is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. The method resulted in spectra that have reduced window smearing for a given window length relative to the discrete Fourier transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to the short time Fourier transform and the continuous wavelet transform. The reduction in spectral smoothing enables better determination of the spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the short time Fourier transform increases as window length decreases. As compared with the continuous wavelet transform, the method has greatly improved temporal resolution, particularly at low frequencies.

scholarly journals Area-Efficient Short-Time Fourier Transform Processor for Time–Frequency Analysis of Non-Stationary Signals

2020 ◽  
Vol 10 (20) ◽  
pp. 7208
Author(s):  
Hohyub Jeon ◽  
Yongchul Jung ◽  
Seongjoo Lee ◽  
Yunho Jung
Keyword(s):  
Fourier Transform ◽  
Real Time ◽  
Frequency Analysis ◽  
Path Delay ◽  
Window Length ◽  
Short Time Fourier Transform ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Stationary Signals ◽  
Short Time

In this paper, we propose an area-efficient short-time Fourier transform (STFT) processor that can perform time–frequency analysis of non-stationary signals in real time, which is essential for voice or radar-signal processing systems. STFT processors consist of a windowing module and a fast Fourier transform processor. The length of the window function is related to the time–frequency resolution, and the required window length varies depending on the application. In addition, the window function needs to overlap the input data samples to minimize the data loss in the window boundary, and overlap ratios of 25%, 50%, and 75% are generally used. Therefore, the STFT processor should ideally support a variable window length and overlap ratio and be implemented with an efficient hardware architecture for real-time time–frequency analysis. The proposed STFT processor is based on the radix-4 multi-path delay commutator (R4MDC) pipeline architecture and supports a variable length of 16, 64, 256, and 1024 and overlap ratios of 25%, 50%, and 75%. Moreover, the proposed STFT processor can be implemented with very low complexity by having a relatively lower number of delay elements, which are the ones that increase complexity in the most STFT processors. The proposed STFT processor was designed using hardware description language (HDL) and synthesized to gate-level circuits using a standard cell library in a 65 nm CMOS process. The proposed STFT processor results in logic gates of 197,970, which is 63% less than that of the conventional radix-2 single-path delay feedback (R2SDF) based STFT processor.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

scholarly journals Ultrasonic Assessment of Thickness and Bonding Quality of Coating Layer Based on Short-Time Fourier Transform and Convolutional Neural Networks

Coatings ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 909
Author(s):  
Azamatjon Kakhramon ugli Malikov ◽  
Younho Cho ◽  
Young H. Kim ◽  
Jeongnam Kim ◽  
Junpil Park ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Coating Layer ◽  
Ultrasonic Pulse ◽  
Short Time Fourier Transform ◽  
Coating Materials ◽  
Time Frequency ◽  
High Attenuation ◽  
Bonding State ◽  
The Time Domain ◽  
Short Time

Ultrasonic non-destructive analysis is a promising and effective method for the inspection of protective coating materials. Offshore coating exhibits a high attenuation rate of ultrasonic energy due to the absorption and ultrasonic pulse echo testing becomes difficult due to the small amplitude of the second echo from the back wall of the coating layer. In order to address these problems, an advanced ultrasonic signal analysis has been proposed. An ultrasonic delay line was applied due to the high attenuation of the coating layer. A short-time Fourier transform (STFT) of the waveform was implemented to measure the thickness and state of bonding of coating materials. The thickness of the coating material was estimated by the projection of the STFT into the time-domain. The bonding and debonding of the coating layers were distinguished using the ratio of the STFT magnitude peaks of the two subsequent wave echoes. In addition, the advantage of the STFT-based approach is that it can accurately and quickly estimate the time of flight (TOF) of a signal even at low signal-to-noise ratios. Finally, a convolutional neural network (CNN) was applied to automatically determine the bonding state of the coatings. The time–frequency representation of the waveform was used as the input to the CNN. The experimental results demonstrated that the proposed method automatically determines the bonding state of the coatings with high accuracy. The present approach is more efficient compared to the method of estimating bonding state using attenuation.

A Modified S-Transform for EEG Signals Analysis

2015 ◽  
Vol 12 (03) ◽  
pp. 1550021 ◽  
Author(s):  
M. A. Al-Manie ◽  
W. J. Wang
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Energy Concentration ◽  
Biomedical Data ◽  
Short Time Fourier Transform ◽  
Phase Information ◽  
Eeg Signals ◽  
Time Frequency ◽  
S Transform ◽  
Short Time

Due to the advantages offered by the S-transform (ST) distribution, it has been recently successfully implemented for various applications such as seismic and image processing. The desirable properties of the ST include a globally referenced phase as the case with the short time Fourier transform (STFT) while offering a higher spectral resolution as the wavelet transform (WT). However, this estimator suffers from some inherent disadvantages seen as poor energy concentration with higher frequencies. In order to improve the performance of the distribution, a modification to the existing technique is proposed. Additional parameters are proposed to control the window's width which can greatly enhance the signal representation in the time–frequency plane. The new estimator's performance is evaluated using synthetic signals as well as biomedical data. The required features of the ST which include invertability and phase information are still preserved.

Classification of Parkinson's Disease from Smartphone Recording Data using Time-Frequency Analysis and Convolutional Neural Network (Preprint)

2021 ◽  
Author(s):  
Denchai Worasawate ◽  
Warisara Asawaponwiput ◽  
Natsue Yoshimura ◽  
Apichart Intarapanich ◽  
Decho Surangsrirat
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Fourier Transform ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Non Invasive ◽  
The Central Nervous System ◽  
Short Time ◽  
The Voice

BACKGROUND Parkinson’s disease (PD) is a long-term neurodegenerative disease of the central nervous system. The current diagnosis is dependent on clinical observation and the abilities and experience of a trained specialist. One of the symptoms that affect most patients over the course of their illness is voice impairment. OBJECTIVE Voice is one of the non-invasive data that can be collected remotely for diagnosis and disease progression monitoring. In this study, we analyzed voice recording data from a smartphone as a possible disease biomarker. The dataset is from one of the largest mobile PD studies, the mPower study. METHODS A total of 29,798 audio clips from 4,051 participants were used for the analysis. The voice recordings were from sustained phonation by the participant saying /aa/ for ten seconds into the iPhone microphone. The audio samples were converted to a spectrogram using a short-time Fourier transform. CNN models were then applied to classify the samples. RESULTS A total of 29,798 audio clips from 4,051 participants were used for the analysis. The voice recordings were from sustained phonation by the participant saying /aa/ for ten seconds into the iPhone microphone. The audio samples were converted to a spectrogram using a short-time Fourier transform. CNN models were then applied to classify the samples. CONCLUSIONS Classification accuracies of the proposed method with LeNet-5, ResNet-50, and VGGNet-16 are 97.7 ± 0.1%, 98.6 ± 0.2%, and 99.3 ± 0.1%, respectively. CLINICALTRIAL ClinicalTrials.gov NCT02696603; https://www.clinicaltrials.gov/ct2/show/NCT02696603

scholarly journals Inverting spectrogram measurements via aliased Wigner distribution deconvolution and angular synchronization

2020 ◽  
Author(s):  
Michael Perlmutter ◽  
Sami Merhi ◽  
Aditya Viswanathan ◽  
Mark Iwen
Keyword(s):  
Fourier Transform ◽  
Phase Retrieval ◽  
Wigner Distribution ◽  
Short Time Fourier Transform ◽  
Fourier Inversion ◽  
New Class ◽  
Bandlimited Signals ◽  
Rank One ◽  
Noise Robust ◽  
Short Time

Abstract We propose a two-step approach for reconstructing a signal $\textbf x\in \mathbb{C}^d$ from subsampled discrete short-time Fourier transform magnitude (spectogram) measurements: first, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix $\widehat{\textbf{x}}\widehat{\textbf{x}}^{*}.$ Secondly, we use angular synchronization to solve for $\widehat{\textbf{x}}$ (and then for $\textbf{x}$ by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and also prove two theorems; one which guarantees the recovery of discrete, bandlimited signals $\textbf{x}\in \mathbb{C}^{d}$ from fewer than $d$ short-time Fourier transform magnitude measurements and another which establishes a new class of deterministic coded diffraction pattern measurements which are guaranteed to allow efficient and noise robust recovery.

scholarly journals Feature Extraction of Impulse Faults for Vibration Signals Based on Sparse Non-Negative Tensor Factorization

2019 ◽  
Vol 9 (18) ◽  
pp. 3642
Author(s):  
Lin Liang ◽  
Haobin Wen ◽  
Fei Liu ◽  
Guang Li ◽  
Maolin Li
Keyword(s):  
Feature Extraction ◽  
Fourier Transform ◽  
Mechanical Equipment ◽  
Tensor Factorization ◽  
Short Time Fourier Transform ◽  
Vibration Signals ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Value Decomposition ◽  
Short Time

The incipient damages of mechanical equipment excite weak impulse vibration, which is hidden, almost unobservable, in the collected signal, making fault detection and failure prevention at the inchoate stage rather challenging. Traditional feature extraction techniques, such as bandpass filtering and time-frequency analysis, are suitable for matrix processing but challenged by the higher-order data. To tackle these problems, a novel method of impulse feature extraction for vibration signals, based on sparse non-negative tensor factorization is presented in this paper. Primarily, the phase space reconstruction and the short time Fourier transform are successively employed to convert the original signal into time-frequency distributions, which are further arranged into a three-way tensor to obtain a time-frequency multi-aspect array. The tensor is decomposed by sparse non-negative tensor factorization via hierarchical alternating least squares algorithm, after which the latent components are reconstructed from the factors by the inverse short time Fourier transform and eventually help extract the impulse feature through envelope analysis. For performance verification, the experimental analysis on the bearing datasets and the swashplate piston pump has confirmed the effectiveness of the proposed method. Comparisons to the traditional methods, including maximum correlated kurtosis deconvolution, singular value decomposition, and maximum spectrum kurtosis, also suggest its better performance of feature extraction.

scholarly journals Zeros of the Wigner distribution and the short-time Fourier transform

2019 ◽  
Vol 33 (3) ◽  
pp. 723-744 ◽  
Author(s):  
Karlheinz Gröchenig ◽  
Philippe Jaming ◽  
Eugenia Malinnikova
Keyword(s):  
Fourier Transform ◽  
Bessel Functions ◽  
Wigner Distribution ◽  
Short Time Fourier Transform ◽  
Step Functions ◽  
Wigner Distributions ◽  
Hurwitz Polynomials ◽  
Totally Positive ◽  
Short Time ◽  
Positive Functions

AbstractWe study the question under which conditions the zero set of a (cross-) Wigner distribution W(f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions. The results require elements from the theory of totally positive functions, Bessel functions, and Hurwitz polynomials. The question of zero-free Wigner distributions is also related to Hudson’s theorem for the positivity of the Wigner distribution and to Hardy’s uncertainty principle. We then construct a class of step functions S so that the Wigner distribution $$W(f,\mathbf {1}_{(0,1)})$$ W ( f , 1 ( 0 , 1 ) ) always possesses a zero $$f\in S \cap L^p$$ f ∈ S ∩ L p when $$p<\infty $$ p < ∞ , but may be zero-free for $$f\in S \cap L^\infty $$ f ∈ S ∩ L ∞ . The examples show that the question of zeros of the Wigner distribution may be quite subtle and relate to several branches of analysis.

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