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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 ..."
Abstract

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.
WideAngle ISAR Passive Imaging Using Smoothed Pseudo WignerVille Distribution
 IEEE Radar Conference Proceedings
, 2001
"... reflected TV signals. UHFband TSAR imaging requires wideangle data to produce good crossrange resolution. We show that direct Fourier reconstruction (DFR) causes degradation of the reconstructed image due to aspectdependent scattering. We find that a Smoothed Pseudo WignerVille distribution (SP ..."
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Cited by 4 (0 self)
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reflected TV signals. UHFband TSAR imaging requires wideangle data to produce good crossrange resolution. We show that direct Fourier reconstruction (DFR) causes degradation of the reconstructed image due to aspectdependent scattering. We find that a Smoothed Pseudo WignerVille distribution (SPWVD) applied in the crossrange direction in place of the Fourier transform can generate a sequence of images, which shows the target reflectivity as a function of aspect angle. Compared to DFR results, these images have higher crossrange resolution. A final image can be synthesized from these images and used for target recogni tion. XPATCH is used to simulate monostatic data from an aircraft. The proposed SPWVDbased imaging method produces a useful image of the aircraft from this data.
Multistatic Passive Radar Imaging Using The Smoothed Pseudo WignerVille Distribution
 in Proc. IEEE Intl. Conf. on Image Processing
, 2001
"... We investigate passive radar imaging of aircraft using reflected TV signals. We apply a Smoothed Pseudo WignerVille Distribution (SPWVD)based SAR imaging algorithm to two different scenarios. In the first simulation, multistatic VHFband dataset generated by Fast Illinois Solver Code (FISC) is used ..."
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Cited by 2 (0 self)
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We investigate passive radar imaging of aircraft using reflected TV signals. We apply a Smoothed Pseudo WignerVille Distribution (SPWVD)based SAR imaging algorithm to two different scenarios. In the first simulation, multistatic VHFband dataset generated by Fast Illinois Solver Code (FISC) is used. In the second simulation, a more realistic simulated passive radar dataset is used. A set of instantaneous images are produced by our algorithm, which have higher resolution and show more detail and features of the aircraft than can be obtained by Direct Fourier Reconstruction (DFR). The set of images provides visually more information about the target and helps to estimate its shape and features. This study suggests that the SPWVDbased imaging might be useful in passive radar imaging and target classification. 1.
Focusing bistatic SAR data using the nonlinear chirp scaling algorithm
 IEEE Trans. Geosci. Remote Sens
"... Abstract—Bistatic synthetic aperture radar data are more challenging to process than the common monostatic counterparts because the flight geometry is more complicated and the data are usually nonstationary. Whereas timedomain algorithms can handle general bistatic cases, they are very inefficient; ..."
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Cited by 2 (0 self)
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Abstract—Bistatic synthetic aperture radar data are more challenging to process than the common monostatic counterparts because the flight geometry is more complicated and the data are usually nonstationary. Whereas timedomain algorithms can handle general bistatic cases, they are very inefficient; therefore, frequencydomain methods are preferred. Several frequencydomain monostatic algorithms have been modified to handle a limited number of bistatic cases, but a general algorithm is sought, which can handle cases such as nonequal platform velocities, nonparallel flight tracks, and high squints. In this paper, we modify the nonlinear chirp scaling (NLCS) algorithm to handle a general case of bistatic data. The key is to use a linear range cell migration correction to reduce the rangeazimuth coupling, an NLCS to precondition the data for azimuth compression, and a series expansion to obtain an accurate form of the signal spectrum. The azimuth nonstationarity is handled through the use of invariance regions. Simulations have shown that the modified NLCS algorithm can handle data with more complicated bistatic geometries than the previous algorithms. Index Terms—Bistatic SAR, chirp scaling, perturbation function, point target response, range cell migration (RCM) correction (RCMC), secondary range compression (SRC), synthetic aperture radar (SAR). I.
A Massively Parallel Spotlight Synthetic Aperture Radar Digital Processor
, 1993
"... A spotlight synthetic aperture radar digital processor has been implemented on an nCUBE 2 parallel supercomputer at Sandia National Laboratories. The digital processor consists of three principal components: a polar reformatter, a twodimensional fast Fourier transformation code, including Taylor we ..."
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A spotlight synthetic aperture radar digital processor has been implemented on an nCUBE 2 parallel supercomputer at Sandia National Laboratories. The digital processor consists of three principal components: a polar reformatter, a twodimensional fast Fourier transformation code, including Taylor weighting [1] for sidelobe reduction, and a phase gradient autofocus [2] code. Several components of the digital processor have also been implemented on other parallel computers including a CM2, an Intel iPSC/860 , and a Cray YMP/1. The performance of the radar processor on all of these machines is discussed.