Uncertainty principles associated with the directional short-time Fourier transform

2021 ◽  
Vol 62 (6) ◽  
pp. 063511
Author(s):  
Hatem Mejjaoli ◽  
Firdous A. Shah
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principles ◽  
Short Time Fourier Transform ◽  
Short Time

Dispersion’s Uncertainty Principles Associated with the Directional Short-Time Fourier Transform

2020 ◽  
Vol 57 (4) ◽  
pp. 508-540
Author(s):  
Siwar Hkimi ◽  
Hatem Mejjaoli ◽  
Slim Omri
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Price Uncertainty ◽  
Uncertainty Principles ◽  
Short Time Fourier Transform ◽  
Short Time

We introduce the directional short-time Fourier transform for which we prove a new Plancherel’s formula. We also prove for this transform several uncertainty principles as Heisenberg inequalities, logarithmic uncertainty principle, Faris–Price uncertainty principles and Donoho–Stark’s uncertainty principles.

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.

An efficient short-time Fourier transform algorithm for grinding wheel condition monitoring through acoustic emission

2021 ◽  
Vol 113 (1-2) ◽  
pp. 585-603
Author(s):  
Wenderson N. Lopes ◽  
Pedro O. C. Junior ◽  
Paulo R. Aguiar ◽  
Felipe A. Alexandre ◽  
Fábio R. L. Dotto ◽  
...  
Keyword(s):  
Acoustic Emission ◽  
Fourier Transform ◽  
Condition Monitoring ◽  
Grinding Wheel ◽  
Short Time Fourier Transform ◽  
Short Time

Fourier Transform and Short-Time Fourier Transform Decomposition for Photovoltaic Arc Fault Detection

2020 ◽  
Author(s):  
Rahul Balamurugan ◽  
Fatima Al-Janahi ◽  
Oumaima Bouhali ◽  
Sawsan Shukri ◽  
Kais Abdulmawjood ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fault Detection ◽  
Short Time Fourier Transform ◽  
Short Time

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.

scholarly journals Fault Detection in DC Microgrids Using Short-Time Fourier Transform

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 277
Author(s):  
Ivan Grcić ◽  
Hrvoje Pandžić ◽  
Damir Novosel
Keyword(s):  
Fourier Transform ◽  
Fault Detection ◽  
Operating Conditions ◽  
Time Signal ◽  
Short Time Fourier Transform ◽  
Dc Microgrid ◽  
Protection Scheme ◽  
Simulink Model ◽  
Battery Energy ◽  
Short Time

Fault detection in microgrids presents a strong technical challenge due to the dynamic operating conditions. Changing the power generation and load impacts the current magnitude and direction, which has an adverse effect on the microgrid protection scheme. To address this problem, this paper addresses a field-transform-based fault detection method immune to the microgrid conditions. The faults are simulated via a Matlab/Simulink model of the grid-connected photovoltaics-based DC microgrid with battery energy storage. Short-time Fourier transform is applied to the fault time signal to obtain a frequency spectrum. Selected spectrum features are then provided to a number of intelligent classifiers. The classifiers’ scores were evaluated using the F1-score metric. Most classifiers proved to be reliable as their performance score was above 90%.

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