The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition

1992 ◽  
Vol 40 (3) ◽  
pp. 559-570 ◽  
Author(s):  
D.J. Wingham
Keyword(s):  
Fourier Transform ◽  
Singular Value Decomposition ◽  
Finite Number ◽  
Singular Value ◽  
Limited Function ◽  
Band Limited ◽  
Band Limited Function ◽  
Value Decomposition

scholarly journals Image analysis of the tree test using wavelet transform, singular value decomposition, and Fourier transform

2019 ◽  
Vol 90 (3) ◽  
pp. 284-293
Author(s):  
Keita Kawasugi ◽  
Kazuhisa Takemura ◽  
Yumi Iwamitsu ◽  
Hitomi Sugawara ◽  
Sakura Nishizawa ◽  
...  
Keyword(s):  
Image Analysis ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition

A New Algorithm to Compensate Ionosphere Phase Contamination

2014 ◽  
Vol 644-650 ◽  
pp. 4551-4554
Author(s):  
Hui Ai ◽  
Jin Feng Hu ◽  
Wan Ge Li ◽  
Zhi Rong Lin ◽  
Ya Xuan Zhang
Keyword(s):  
Fourier Transform ◽  
Singular Value Decomposition ◽  
Prior Information ◽  
Hankel Matrix ◽  
Singular Value ◽  
Echo Signal ◽  
Rank Reduction ◽  
Coherent Integration ◽  
Priori Information ◽  
Value Decomposition

The echo signals of sky-wave over-the-horizon radar involve ionospheric phase contamination with spectrum expansion. The bragg peaks expand and cover the frequency spectrum of low speed target. So ionospheric phase decontamination is necessary before coherent integration. The traditional Hankel Rank Reduction (HRR) phase decontamination method constructs the Hankel matrix by folding the echo signal, estimating instantaneous frequency through singular value decomposition. But HRR method requires the prior information of signal components. The estimation is invalid without priori information. The algorithm presented in this paper does not require the priori information. The algorithm based on matched fourier transform can accurately estimate the phase contamination function for the clutter noise ratio is high. Simulation shows that the proposed algorithm has better performance in phase decontamination.

An Improved Seismic Data Completion Algorithm using Low-Rank Tensor Optimization: Cost Reduction and Optimal Data Orientation

Geophysics ◽  
2021 ◽  
pp. 1-88
Author(s):  
Jonathan Popa ◽  
Susan E. Minkoff ◽  
Yifei Lou
Keyword(s):  
Fourier Transform ◽  
Singular Value Decomposition ◽  
Seismic Data ◽  
Convex Sets ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Low Rank ◽  
Traditional Methods ◽  
Value Decomposition ◽  
Conjugate Symmetry

Seismic data are often incomplete due to equipment malfunction, limited source and receiver placement at near and far offsets, and missing cross-line data. Seismic data contain redundancies as they are repeatedly recorded over the same or adjacent subsurface regions, causing the data to have a low-rank structure. To recover missing data one can organize the data into a multidimensional array or tensor and apply a tensor completion method. We can increase the effectiveness and efficiency of low-rank data reconstruction based on the tensor singular value decomposition (tSVD) by analyzing the effect of tensor orientation and exploiting the conjugate symmetry of the multidimensional Fourier transform. In fact, these results can be generalized to any order tensor. Relating the singular values of the tSVD to those of a matrix leads to a simplified analysis, revealing that the most square orientation gives the best data structure for low-rank reconstruction. After the first step of the tSVD, a multidimensional Fourier transform, frontal slices of the tensor form conjugate pairs. For each pair a singular value decomposition can be replaced with a much cheaper conjugate calculation, allowing for faster computation of the tSVD. Using conjugate symmetry in our improved tSVD algorithm reduces the runtime of the inner loop by 35% to 50%. We consider synthetic and real seismic datasets from the Viking Graben Region and the Northwest Shelf of Australia arranged as high-dimensional tensors. We compare tSVD based reconstruction to traditional methods, projection onto convex sets and multichannel singular spectrum analysis, and see that the tSVD based method gives similar or better accuracy and is more efficient, converging with runtimes that are an order of magnitude faster than the traditional methods. Additionally, we verify the most square orientation improves recovery for these examples by 10-20% compared to the other orientations.

scholarly journals A Tacholess Order Tracking Method Based on Inverse Short Time Fourier Transform and Singular Value Decomposition for Bearing Fault Diagnosis

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6924
Author(s):  
Lang Xu ◽  
Steven Chatterton ◽  
Paolo Pennacchi ◽  
Chang Liu
Keyword(s):  
Fourier Transform ◽  
Singular Value Decomposition ◽  
Rotation Frequency ◽  
Singular Value ◽  
Target Component ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Order Tracking ◽  
Value Decomposition ◽  
Short Time

Order tracking has been widely used to diagnose failures of variable speed rotating machines. The performance of the TOT (Time-Frequency Domain Tacholess Order Tracking) methods is based on the correct separation of the target component strictly related to the shaft rotation frequency. Currently, most of the methods have focused on obtaining the instantaneous frequency with accuracy. In this paper, a new TOT method has been proposed that combines the inverse short-time Fourier transform (ISTFT) with singular value decomposition (SVD). The target component closely related to the shaft rotation frequency is selected and filtered approximately in the time-frequency domain. Hence, the ISTFT is adopted to reverse the target component into the time domain. Next, SVD is used to refine the roughly filtered target component. Finally, the phase of the refined signal is extracted to resample the original signal. The performance of the method was tested using real vibration signals collected from a large-scale test rig of a high-speed train traction system.

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