scholarly journals On the Quaternionic Short-Time Fourier and Segal–Bargmann Transforms

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Antonino De Martino ◽  
Kamal Diki
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Reproducing Kernel ◽  
Short Time Fourier Transform ◽  
Reconstruction Formula ◽  
Bargmann Transform ◽  
One Dimensional ◽  
Basic Properties ◽  
Bargmann Transforms ◽  
Short Time

AbstractIn this paper, we study a special one-dimensional quaternion short-time Fourier transform (QSTFT). Its construction is based on the slice hyperholomorphic Segal–Bargmann transform. We discuss some basic properties and prove different results on the QSTFT such as Moyal formula, reconstruction formula and Lieb’s uncertainty principle. We provide also the reproducing kernel associated with the Gabor space considered in this setting.

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 Localization Operators and an Uncertainty Principle for the Discrete Short Time Fourier Transform

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Carmen Fernández ◽  
Antonio Galbis ◽  
Josep Martínez
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Extremal Functions ◽  
Short Time Fourier Transform ◽  
Localization Operators ◽  
Time Frequency ◽  
Short Time ◽  
Frequency Basis ◽  
Discrete Setting

Localization operators in the discrete setting are used to obtain information on a signalffrom the knowledge on the support of its short time Fourier transform. In particular, the extremal functions of the uncertainty principle for the discrete short time Fourier transform are characterized and their connection with functions that generate a time-frequency basis is studied.

Analysis on Weak Signals with Short-Time Fourier Transform Method

2014 ◽  
Vol 556-562 ◽  
pp. 5003-5005 ◽  
Author(s):  
Qi Da Yu ◽  
Ya Lin Li ◽  
Jin Wang
Keyword(s):  
Fourier Transform ◽  
Diagnostic Methods ◽  
Diagnostic Efficiency ◽  
Analysis Method ◽  
Short Time Fourier Transform ◽  
Weak Signals ◽  
Transform Method ◽  
Fourier Transform Method ◽  
One Dimensional ◽  
Short Time

To make easy for the operators on the work of analyzing the weak signals, at the same time, for the purpose to improve unskillful operators analyze ability and diagnostic efficiency, at last to get the goal of fast diagnostic. Methods: We recommend STFT theory, then analyzed algorithm to design the programs by the way of LabVIEW2011, at last we realized to change one-dimensional weak signals into the form of intensity maps, which owns obvious recognition feature. Results: We have successfully used programs to realize the analysis on intensity maps, and also simplified judgmental process on illness. This method improves efficiency. Conclusion: Using the method described above can achieve the goal for improving the analysis method, it may work well as we thought before.

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
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