Gaussian Window of Optimal Time-Frequency Resolution in Numerical Implementation of Short-Time Fourier Transform

2011 ◽  
Vol 48-49 ◽  
pp. 555-560 ◽  
Author(s):  
Yang Jin ◽  
Zhi Yong Hao
Keyword(s):  
Fourier Transform ◽  
Continuous Time ◽  
Gaussian Function ◽  
Frequency Resolution ◽  
Optimal Time ◽  
Numerical Implementation ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Gaussian Window ◽  
Short Time

In this paper, we report the condition to keep the optimal time-frequency resolution of the Gaussian window in the numerical implementation of the short-time Fourier transform. Because of truncation and discretization, the time-frequency resolution of the discrete Gaussian window is different from that of the proper Gaussian function. We compared the time-frequency resolution performance of the discrete Gaussian window and Hanning window based on that they have the same continuous-time domain standard deviation, and generalized the condition under which the time-frequency resolution of the Gaussian window will prevail over that of the Hanning window.

The Time-Frequency Resolution of Short Time Fourier Transform Based on Multi-Window Functions

2011 ◽  
Vol 214 ◽  
pp. 122-127 ◽  
Author(s):  
Li Hua Wang ◽  
Qi Dong Zhang ◽  
Yong Hong Zhang ◽  
Kai Zhang
Keyword(s):  
Fourier Transform ◽  
Time Resolution ◽  
High Performance ◽  
Frequency Resolution ◽  
Good Time ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Window Functions ◽  
Short Time ◽  
Good Time Resolution

The short-time Fourier transform has the disadvantage that is does not localize time and frequency phenomena very well. Instead the time-frequency information is scattered which depends on the length of the window. It is not possible to have arbitrarily good time resolution simultaneously with good frequency resolution. In this paper, a new method that uses the short-time Fourier transform based on multi-window functions to enhance time-frequency resolution of signals has been proposed. Simulation and experimental results present the high performance of the proposed method.

scholarly journals A Study of Parameters Setting of the STADZT

10.14311/1654 ◽  
2012 ◽  
Vol 52 (5) ◽  
Author(s):  
Václav Turoň
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Stationary Signals ◽  
Zolotarev Polynomials ◽  
Non Stationary Signal ◽  
Short Time ◽  
Main Influence

This paper deals with the new time-frequency Short-Time Approximated Discrete Zolotarev Transform (STADZT), which is based on symmetrical Zolotarev polynomials. Due to the special properties of these polynomials, STADZT can be used for spectral analysis of stationary and non-stationary signals with the better time and frequency resolution than the widely used Short-Time Fourier Transform (STFT). This paper describes the parameters of STADZT that have the main influence on its properties and behaviour. The selected parameters include the shape and length of the segmentation window, and the segmentation overlap. Because STADZT is very similar to STFT, the paper includes a comparison of the spectral analysis of a non-stationary signal created by STADZT and by STFT with various settings of the parameters.

scholarly journals An Adaptive Resolution Computationally Efficient Short-Time Fourier Transform

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Saeed Mian Qaisar ◽  
Laurent Fesquet ◽  
Marc Renaudin
Keyword(s):  
Fourier Transform ◽  
Input Signal ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Computationally Efficient ◽  
Time Frequency ◽  
Adaptive Resolution ◽  
Processing Power ◽  
Short Time

The short-time Fourier transform (STFT) is a classical tool, used for characterizing the time varying signals. The limitation of the STFT is its fixed time-frequency resolution. Thus, an enhanced version of the STFT, which is based on the cross-level sampling, is devised. It can adapt the sampling frequency and the window function length by following the input signal local characteristics. Therefore, it provides an adaptive resolution time-frequency representation of the input signal. The computational complexity of the proposed STFT is deduced and compared to the classical one. The results show a significant gain of the computational efficiency and hence of the processing power.

Seismic spectral decomposition using deconvolutive short-time Fourier transform spectrogram

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. V43-V51 ◽  
Author(s):  
Wenkai Lu ◽  
Fangyu Li
Keyword(s):  
Fourier Transform ◽  
Spectral Decomposition ◽  
Reservoir Characterization ◽  
Low Frequency ◽  
Seismic Signal ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Distribution Method ◽  
Time Frequency ◽  
Short Time

The spectral decomposition technique plays an important role in reservoir characterization, for which the time-frequency distribution method is essential. The deconvolutive short-time Fourier transform (DSTFT) method achieves a superior time-frequency resolution by applying a 2D deconvolution operation on the short-time Fourier transform (STFT) spectrogram. For seismic spectral decomposition, to reduce the computation burden caused by the 2D deconvolution operation in the DSTFT, the 2D STFT spectrogram is cropped into a smaller area, which includes the positive frequencies fallen in the seismic signal bandwidth only. In general, because the low-frequency components of a seismic signal are dominant, the removal of the negative frequencies may introduce a sharp edge at the zero frequency, which would produce artifacts in the DSTFT spectrogram. To avoid this problem, we used the analytic signal, which is obtained by applying the Hilbert transform on the original real seismic signal, to calculate the STFT spectrogram in our method. Synthetic and real seismic data examples were evaluated to demonstrate the performance of the proposed method.

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 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.

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