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24
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 121 (22 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.
Accelerating the nonuniform Fast Fourier Transform
 SIAM REVIEW
, 2004
"... The nonequispaced Fourier transform arises in a variety of application areas, from medical imaging to radio astronomy to the numerical solution of partial differential equations. In a typical problem, one is given an irregular sampling of N data in the frequency domain and one is interested in recon ..."
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Cited by 70 (4 self)
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The nonequispaced Fourier transform arises in a variety of application areas, from medical imaging to radio astronomy to the numerical solution of partial differential equations. In a typical problem, one is given an irregular sampling of N data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain. When the sampling is uniform, the fast Fourier transform (FFT) allows this calculation to be computed in O(N log N) operations rather than O(N 2) operations. Unfortunately, when the sampling is nonuniform, the FFT does not apply. Over the last few years, a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform FFTs (NUFFTs). These rely on a mixture of interpolation and the judicious use of the FFT on an oversampled grid [A. Dutt and V. Rokhlin, SIAM J. Sci. Comput., 14 (1993), pp. 1368–1383]. In this paper, we observe that one of the standard interpolation or “gridding ” schemes, based on Gaussians, can be accelerated by a significant factor without precomputation and storage of the interpolation weights. This is of particular value in two and threedimensional settings, saving either 10dN in storage in d dimensions or a factor of about 5–10 in CPUtime (independent of dimension).
Fast Fourier transform of sparse spatial data to sparse Fourier data
 Proc. 2000 IEEE Antennas and Propagation Society Int. Symp
, 2000
"... (*Dedicated to the memory of my mother who labored all her life for the next generation.) 1. ..."
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Cited by 8 (1 self)
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(*Dedicated to the memory of my mother who labored all her life for the next generation.) 1.
New BehavioralLevel Simulation Technique for RF/Microwave Applications. Part III: Advanced Concepts
, 2001
"... ABSTRACT: The quadrature modeling structure is widely accepted as an efficient tool for the nonlinear simulation of RF/microwave bandpass stages (power amplifiers, etc.) for wireless applications. The common belief is that this structure can be applied to model only bandpass memoryless nonlinearitie ..."
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Cited by 4 (4 self)
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ABSTRACT: The quadrature modeling structure is widely accepted as an efficient tool for the nonlinear simulation of RF/microwave bandpass stages (power amplifiers, etc.) for wireless applications. The common belief is that this structure can be applied to model only bandpass memoryless nonlinearities (which, however, may exhibit amplitudetophase conversion). In two recent articles [1, 2] the authors have extended the application of the quadrature modeling structure to modeling broadband nonlinearities, which makes possible to predict harmonics and evenorder nonlinearities, to take into account the frequency response, etc. This article completes the overview of the instantaneous quadrature technique. The authors discuss its application to modeling AM, FM and PM detectors, which are strongly nonlinear elements with large memory (both the strong nonlinearity and large memory effects are essential for the detector proper operation), thus removing the limitation of nonlinearity to be memoryless or quasimemoryless. The identification of nonlinear interference/distortion sources is of great relevance for a practical EMC/EMI design. In the second part of this article, we discuss the dichotomous identification method, which is much more computationally efficient than a simple singlesignal method, especially for a large number of input signals. Individual spectral components of a complexspectrum signal can also be considered as input signals and, hence, it is possible to identify the spectral components responsible for a particular nonlinear interference/distortion (say, for a particular
Exploring parallelization strategies for NUFFT data translation
 in Proc. of the ACM International Conf. on Embedded Software
, 2009
"... This paper introduces parallelization strategies for the NonUniform FFT (NUFFT) data translation on multicore architectures. The NUFFT enables the use of the celebrated FFT with unequally spaced data in numerous situations in signal and image processing as well as in scientific computing. The cr ..."
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Cited by 3 (2 self)
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This paper introduces parallelization strategies for the NonUniform FFT (NUFFT) data translation on multicore architectures. The NUFFT enables the use of the celebrated FFT with unequally spaced data in numerous situations in signal and image processing as well as in scientific computing. The critical extension lies at the translation of nonequally spaced or nonuniformly sampled data onto an equally spaced Cartesian grid or vice versa. The data translation can be made sufficiently accurate, with the arithmetic complexity linearly proportional to the size of the data ensemble. For large NUFFTs, however, the data translation is found substantially dominant in computation time on modern computers while it is expected to be dominated by the FFT. In order to match the FFT performance achieved by FFTW, data locality and parallelism in the data translation must be explored and exploited as well. We are concerned with two fundamental issues. First, the data translation can be described as a matrixvector multiplication with a matrix of irregular sparsity. This is beyond the effective scope of the conventional tiling and parallelization schemes applied by a compiler for performance improvement on computation with dense matrices. Secondly, multicore processors exist and emerge in many different configurations, and are expected to evolve further in architectural variety. This may mean the end of performance tuning on a single type of architecture. In this paper, we introduce an automation tool that takes two specifications as input, one on an applicationspecific data translation algorithm, the other on a target multicore processor architecture. The tool generates a parallel code that explores the data locality and parallelism by utilizing both geometric structures in data translation and the processormemory configurations in the target architec
Scalable Mismatch Correction for Timeinterleaved AnalogtoDigital Converters in OFDM Reception” , technical report available at http://www.ece.ucsb.edu/wcsl/publications.html
"... Abstract—Realization of alldigital baseband receiver processing for multiGigabit communication requires analogtodigital converters (ADCs) of sufficient rate and output resolution. A promising architecture for this purpose is the timeinterleaved ADC (TIADC), in which L “subADCs ” are employed ..."
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Cited by 2 (2 self)
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Abstract—Realization of alldigital baseband receiver processing for multiGigabit communication requires analogtodigital converters (ADCs) of sufficient rate and output resolution. A promising architecture for this purpose is the timeinterleaved ADC (TIADC), in which L “subADCs ” are employed in parallel. However, the gain, timing and voltageoffset mismatches between the subADCs, if left uncompensated, lead to error floors in receiver performance. A standard technique for gain and timing mismatch correction is to use L FIR filters, with tap lengths increasing with the mismatch levels. In this paper, we investigate the use of TIADCs in OFDM receivers, and provide a scalable technique for mismatch compensation whose complexity is independent of L and the mismatch levels. We achieve this by decomposing the FFT operator that is at the core of the OFDM receiver into eigenmodes, and showing that, even for large values of L and mismatch levels as high as 25%, two eigenmodes suffice to provide an accurate description of the mismatchperturbed FFT operator. We provide simulation results that show that the associated mismatch compensation algorithm is successful is eliminating the mismatchinduced error floor. I.
Scalable Parallelization Strategies to Accelerate NuFFT Data Translation on Multicores
"... Abstract. The nonuniform FFT (NuFFT) has been widely used in many applications. In this paper, we propose two new scalable parallelization strategies to accelerate the data translation step of the NuFFT on multicore machines. Both schemes employ geometric tiling and binning to exploit data localit ..."
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Cited by 2 (1 self)
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Abstract. The nonuniform FFT (NuFFT) has been widely used in many applications. In this paper, we propose two new scalable parallelization strategies to accelerate the data translation step of the NuFFT on multicore machines. Both schemes employ geometric tiling and binning to exploit data locality, and use recursive partitioning and scheduling with dynamic task allocation to achieve load balancing. The experimental results collected from a commercial multicore machine show that, with the help of our parallelization strategies, the data translation step is no longer the bottleneck in the NuFFT computation, even for large data set sizes, with any input sample distribution. 1
THROUGH WALL IMAGING WITH UWB RADAR SYSTEM
, 2009
"... Supervisor: doc. Ing. Miloˇs Drutarovsk´y, CSc. ”If we save even one life, we have been cost effective.” ..."
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Supervisor: doc. Ing. Miloˇs Drutarovsk´y, CSc. ”If we save even one life, we have been cost effective.”
An Efficient Analysis of Shielded Single and Multiple Coupled Microstrip Lines With the Nonuniform Fast Fourier Transform (NUFFT) Technique
"... nique is incorporated into the spectraldomain approach for the analysis of shielded single and multiple coupled microstrip lines. Each of the spectraldomain Green’s functions is decomposed into an asymptotic part and a remaining part. At the interface of layered dielectrics with conducting strips, ..."
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nique is incorporated into the spectraldomain approach for the analysis of shielded single and multiple coupled microstrip lines. Each of the spectraldomain Green’s functions is decomposed into an asymptotic part and a remaining part. At the interface of layered dielectrics with conducting strips, the product of a basis function and an associated Green’s function constitutes an expansionfield. The inverse Fourier transform (IFT) of the expansionfield is its spatial distribution all over the interface. We take this advantage to match the final boundary conditions on all the conducting strips simultaneously. As a result, if all the strips are at one interface, the number of operations required in this method is proportional to, but not to 2, where is the number of the strips. The IFT of the asymptotic part of each expansionfield can be obtained analytically, and that of the remaining part can be quickly processed by the NUFFT. The Gauss–Chebyshev quadrature is used to accelerate the computations of the integrals resulted from the Galerkin’s procedure. The proposed method is also applied to investigate the dispersion characteristics of coupled lines with finite metallization thickness and of coupled lines at different levels. A convergence analysis of the results is presented and a comparison of used CPU time is discussed. Index Terms—Method of moments (MoM), microstrip lines, nonuniform fast Fourier transform (NUFFT), spectraldomain approach (SDA). I.
Contents List of Abbreviations List of Symbols
"... Thesis to the dissertation examination ..."
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