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 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.

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.

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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