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Nonuniform Fast Fourier Transforms Using MinMax Interpolation
 IEEE Trans. Signal Process
, 2003
"... The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several pap ..."
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Cited by 83 (13 self)
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The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the minmax sense of minimizing the worstcase approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the minmax approach provides substantially lower approximation errors than conventional interpolation methods. The minmax criterion is also useful for optimizing the parameters of interpolation kernels such as the KaiserBessel function.
Random sampling of multivariate trigonometric polynomials
 SIAM J. Math. Anal
, 2004
"... We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(xj) on a random set of points xj in the unit cube (the “sampling problem for trigonometric polynomials”) and estimate the probability distribution of the condition number for th ..."
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Cited by 30 (3 self)
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We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(xj) on a random set of points xj in the unit cube (the “sampling problem for trigonometric polynomials”) and estimate the probability distribution of the condition number for the associated Vandermondetype and Toeplitzlike matrices. The results provide a solid theoretical foundation for some efficient numerical algorithms that are already in use.
Reconstruction of periodic bandlimited signals from nonuniform samples
, 2004
"... I would first like to thank my advisor, Dr. Yonina Eldar, for her support, patience, and shoving me in the right direction in critical moments. Thank you for the knowledge I acquired from you. I feel extremely fortunate to have an advisor like you. Thanks to Prof. Arie Feuer of the Technion–Israel I ..."
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Cited by 3 (2 self)
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I would first like to thank my advisor, Dr. Yonina Eldar, for her support, patience, and shoving me in the right direction in critical moments. Thank you for the knowledge I acquired from you. I feel extremely fortunate to have an advisor like you. Thanks to Prof. Arie Feuer of the Technion–Israel Institute of Technology for first introducing me the field of nonuniform sampling. The initial step for this research was carried out from these fruitful discussions. Thanks to Prof. Amir Averbuch of the Tel Aviv University for raising the issue of stability of the algorithms proposed in this work. This topic stimulated the significant phase of my research. I want to also thank Prof. Michael Unser and Dr. Thierry Blu from EPFL, Swiss, and Dr. Thomas Strohmer from University of California, Davis for valuable suggestions related to this work. Thanks to every member of the research group under the supervision of Dr. Yonina Eldar. Ami, Liron, Zvika, Tsvika, Nagesh, Moshe, and Noam, I thank you all for your friendship, and for all the help through the endless discussions we had.
An realtime algorithm for time decoding machines,” BNET
, 2005
"... Timeencoding is a realtime asynchronous mechanism of mapping the information contained in the amplitude of a bandlimited signal into a time sequence. Time decoding algorithms recover the signal from the time sequence. Under an appropriate Nyquisttype rate condition the signal can be perfectly rec ..."
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Cited by 2 (2 self)
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Timeencoding is a realtime asynchronous mechanism of mapping the information contained in the amplitude of a bandlimited signal into a time sequence. Time decoding algorithms recover the signal from the time sequence. Under an appropriate Nyquisttype rate condition the signal can be perfectly recovered. The algorithm for perfect recovery calls, however, for the computation of a pseudoinverse of an infinite dimensional matrix. We present a simple algorithm for local signal recovery and construct a stitching algorithm for realtime signal recovery. We also provide a recursive algorithm for computing the pseudoinverse of a family of finitedimensional matrices. 1.
Nonuniform Sampling: Exact Reconstruction From Nonuniformly Distributed . . .
, 2002
"... this article, we discuss the problem of reconstructing a function f in a latticeinvariant subspace of L (IR ) from a family of nonuniformly distributed, weightedaverages fhf; x j i : j 2 Jg using an approximationprojection iterative algorithm ..."
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Cited by 1 (0 self)
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this article, we discuss the problem of reconstructing a function f in a latticeinvariant subspace of L (IR ) from a family of nonuniformly distributed, weightedaverages fhf; x j i : j 2 Jg using an approximationprojection iterative algorithm
Fast Recovery Algorithms For Time Encoded Bandlimited Signals
 Proceeding of the International Conference on Acoustics, Speech and Signal Processing (ICASSP’05
, 2004
"... mapping amplitude information into a time sequence. We investigate fast algorithms for the recovery of time encoded bandlimited signals and construct an algorithm that has provably low computational complexity. We also devise a fast algorithm that is parameterinsensitive. ..."
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mapping amplitude information into a time sequence. We investigate fast algorithms for the recovery of time encoded bandlimited signals and construct an algorithm that has provably low computational complexity. We also devise a fast algorithm that is parameterinsensitive.
IMPROVED FREQUENCY DOMAIN SUPERRESOLUTION ALGORITHM WITH CONJUGATE GRADIENT – NUFFT METHOD AS ITS RECONSTRUCTION CORE
"... In the paper frequency domain SuperResolution algorithm with enhanced reconstruction stage is presented. The Fourier transform properties of relocated images are used to easy estimation of rotation and translation, as well as artifacts caused by subsampling. Previously, the bicubic interpolation ha ..."
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In the paper frequency domain SuperResolution algorithm with enhanced reconstruction stage is presented. The Fourier transform properties of relocated images are used to easy estimation of rotation and translation, as well as artifacts caused by subsampling. Previously, the bicubic interpolation has been employed in the reconstruction phase, in this paper it is replaced by iterative conjugategradient method with inverse nonuniform fast Fourier transform at its core. The new algorithm indeed gives improved results, if compared to those of the previous ones. 1.