Characterization of L. Schwartz’ convolutor and multiplier spaces $$\mathcal O _{C}'$$ O C ′ and $$\mathcal O _{M}$$ O M by the short-time Fourier transform

2013 ◽  
Vol 108 (2) ◽  
pp. 833-847 ◽  
Author(s):  
Christian Bargetz ◽  
Norbert Ortner
Keyword(s):  
Fourier Transform ◽  
Short Time Fourier Transform ◽  
Short Time

scholarly journals Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 240
Author(s):  
Sanja Atanasova ◽  
Snježana Maksimović ◽  
Stevan Pilipović
Keyword(s):  
Fourier Transform ◽  
Wave Front ◽  
Short Time Fourier Transform ◽  
Wave Fronts ◽  
Directional Wave ◽  
Tempered Ultradistributions ◽  
Short Time

In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.

scholarly journals Identification of Grain Oriented SiFe Steels Based on Imaging the Instantaneous Dynamics of Magnetic Barkhausen Noise Using Short-Time Fourier Transform and Deep Convolutional Neural Network

Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 118
Author(s):  
Michal Maciusowicz ◽  
Grzegorz Psuj ◽  
Paweł Kochmański
Keyword(s):  
Fourier Transform ◽  
Barkhausen Noise ◽  
Magnetic Barkhausen Noise ◽  
Short Time Fourier Transform ◽  
Deep Convolutional Neural Networks ◽  
Electrical Steels ◽  
New Approach ◽  
Time Frequency ◽  
Short Time

This paper presents a new approach to the extraction and analysis of information contained in magnetic Barkhausen noise (MBN) for evaluation of grain oriented (GO) electrical steels. The proposed methodology for MBN analysis is based on the combination of the Short-Time Fourier Transform for the observation of the instantaneous dynamics of the phenomenon and deep convolutional neural networks (DCNN) for the extraction of hidden information and building the knowledge. The use of DCNN makes it possible to find even complex and convoluted rules of the Barkhausen phenomenon course, difficult to determine based solely on the selected features of MBN signals. During the tests, several samples made of conventional and high permeability GO steels were tested at different angles between the rolling and transverse directions. The influences of the angular resolution and the proposed additional prediction update algorithm on the DCNN accuracy were investigated, obtaining the highest gain for the angle of 3.6°, for which the overall accuracy exceeded 80%. The obtained results indicate that the proposed new solution combining time–frequency analysis and DCNN for the quantification of information from MBN having stochastic nature may be a very effective tool in the characterization of the magnetic materials.

scholarly journals Time-frequency Analysis of Multicomponent LFM signal based on Hough and Chirplet Transform

2018 ◽  
Vol 173 ◽  
pp. 03054
Author(s):  
Xueqin Zhang ◽  
Ruolun Liu
Keyword(s):  
Fourier Transform ◽  
Line Detection ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
Chirplet Transform ◽  
Frequency Map ◽  
Linear Frequency Modulated Signal ◽  
Short Time

The Chirplet Transform (CT) is effective in the characterization of IF for mono-component linear-frequency-modulated signal. However, During the initialization process, using the peak of the time-frequency map of the short-time Fourier transform to fit the line is greatly affected by noise. For the multi-component signals, it is more difficult to distinguish and fit different IF lines. Since the Hough is good at a common algorithm for the line detection, the ridge edge fitting is replaced by the Hough transform in this paper. The experiment results show significant improvement in the obtained time-frequency representation.

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.

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