Showing papers on "Fast Fourier transform published in 1998"
12 May 1998
TL;DR: An adaptive FFT program that tunes the computation automatically for any particular hardware, and tests show that FFTW's self-optimizing approach usually yields significantly better performance than all other publicly available software.
Abstract: FFT literature has been mostly concerned with minimizing the number of floating-point operations performed by an algorithm. Unfortunately, on present-day microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have a larger impact on performance. Consequently, one must know the details of a computer architecture in order to design a fast algorithm. In this paper, we propose an adaptive FFT program that tunes the computation automatically for any particular hardware. We compared our program, called FFTW, with over 40 implementations of the FFT on 7 machines. Our tests show that FFTW's self-optimizing approach usually yields significantly better performance than all other publicly available software. FFTW also compares favorably with machine-specific, vendor-optimized libraries.
1,824 citations
Book•
01 Jan 1998
TL;DR: The Transmission Electron Microscope helps in the calculation of images of Thin and Thick Specimens using the Fourier Projection Theorem and the Bilinear Interpolation.
Abstract: The Transmission Electron Microscope.- Linear Image Approximations.- Sampling and the Fast Fourier Transform.- Calculation of Images of Thin Specimens.- Theory of Calculation of Images of Thick Specimens.- Multislice Applications and Examples.- The Programs.- Plotting Transfer Functions.- The Fourier Projection Theorem.- Atomic Potentials and Scattering Factors.- Bilinear Interpolation.- 3D Perspective View.
937 citations
TL;DR: This article investigates three algorithms for the FFT-accelerated Ewald sum, namely, the so-called particle–particle–part particle mesh (P3M), particle mesh Ewald (PME), and smooth PME method, and proposes a set of combinations of the individual components that it regard to be the most flexible.
Abstract: Standard Ewald sums, which calculate, e.g., the electrostatic energy or the force in periodically closed systems of charged particles, can be efficiently speeded up by the use of the fast Fourier transformation (FFT). In this article we investigate three algorithms for the FFT-accelerated Ewald sum, which have attracted widespread attention, namely, the so-called particle–particle–particle mesh (P3M), particle mesh Ewald (PME), and smooth PME method. We present a unified view of the underlying techniques and the various ingredients which comprise those routines. Additionally, we offer detailed accuracy measurements, which shed some light on the influence of several tuning parameters and also show that the existing methods — although similar in spirit — exhibit remarkable differences in accuracy. We propose a set of combinations of the individual components, mostly relying on the P3M approach, that we regard to be the most flexible. The issue of estimating the errors connected with particle mesh routines is reserved to paper II.
647 citations
Posted Content•
TL;DR: A fast Fourier transform method for synthesizing approximateSelf-similar sample paths for one type of self-similar process, Fractional Gaussian Noise, is presented and it is found that the method is as fast or faster than existing methods and appears to generate close approximations to true self- similar sample paths.
Abstract: Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with self-similar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths for one type of self-similar process, Fractional Gaussian Noise, and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate close approximations to true self-similar sample paths. We also discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series.
404 citations
TL;DR: In this article, a joint time-frequency transform (TFT) was proposed for radar imaging of single and multiple targets with complex motion, where the Doppler spectrum becomes smeared and the image is blurred.
Abstract: Conventional radar imaging uses the Fourier transform to retrieve Doppler information. However, due to the complex motion of a target, the Doppler frequency shifts are actually time-varying. By using the Fourier transform, the Doppler spectrum becomes smeared and the image is blurred. Without resorting to sophisticated motion compensation algorithms, the image blurring problem can be resolved with the joint time-frequency transform. High-resolution time-frequency transforms are investigated, and examples of applications to radar imaging of single and multiple targets with complex motion are given.
349 citations
TL;DR: In this paper, the relationship between two coefficients used in sensitivity analysis of model output is investigated, namely the Fourier amplitude sensitivity test's coefficient and the Sobol' sensitivity indices, developed in the 1990s.
342 citations
29 Sep 1998
TL;DR: By exploiting the spatial regularity of the new algorithm, the requirement for both dominant elements in VLSI implementation, the memory size and the number of complex multipliers, have been minimized and the area/power efficiency has been enhanced.
Abstract: The FFT processor is one of the key components in the implementation of wideband OFDM systems. Architectures with a structured pipeline have been used to meet the fast, real-time processing demand and low-power consumption requirement in a mobile environment. Architectures based on new forms of FFT, the radix-2/sup i/ algorithm derived by cascade decomposition, is proposed. By exploiting the spatial regularity of the new algorithm, the requirement for both dominant elements in VLSI implementation, the memory size and the number of complex multipliers, have been minimized. Progressive wordlength adjustment has been introduced to optimize the total memory size with a given signal-to-quantization-noise-ratio (SQNR) requirement in fixed-point processing. A new complex multiplier based on distributed arithmetic further enhanced the area/power efficiency of the design. A single-chip processor for 1 K complex point FFT transform is used to demonstrate the design issues under consideration.
322 citations
Patent•
24 Feb 1998
TL;DR: In this article, the spectral and spatial components of the adaptive weights are calculated in a unified operation, based on the mathematical analogy between the spectrum and spatial descriptions of the airlink.
Abstract: A discrete multitone stacked-carrier spread spectrum communication method is based on frequency domain spreading including multiplication of a baseband signal by a set of superimposed, or stacked, complex sinusoid carrier waves. In a preferred embodiment, the spreading involves energizing the bins of a large Fast Fourier transform (FFT). This provides a considerable savings in computational complexity for moderate output FFT sizes. Point-to-multipoint and multipoint-to-multipoint (nodeless) network topologies are possible. A code-nulling method is included for interference cancellation and enhanced signal separation by exploiting the spectral diversity of the various sources. The basic method may be extended to include multielement antenna array nulling methods for interference cancellation and enhanced signal separation using spatial separation. Such methods permit directive and retrodirective transmission systems that adapt or can be adapted to the radio environment. Such systems are compatible with bandwidth-on-demand and higher-order modulation formats and use advanced adaptation algorithms. In a specific embodiment the spectral and spatial components of the adaptive weights are calculated in a unified operation based on the mathematical analogy between the spectral and spatial descriptions of the airlink.
318 citations
Journal Article•
TL;DR: The proposed filter is a truncated series expansion of the inverse of that operator that maps object opacity function to hologram intensity, which is shown to be equivalent to conventional (optical) reconstruction, with successive terms increasingly sup-pressing the twin image.
Abstract: Digitally sampled in-line holograms may be linearly filtered to reconstruct a representation of the original object distribution, thereby decoding the information contained in the hologram. The decoding process is performed by digital computation rather than optically. Substitution of digital for optical decoding has several advantages, including selective suppression of the twin-image artifact, elimination of the far-field requirement, and automation of the data reduction and analysis process. The proposed filter is a truncated series expansion of the inverse of that operator that maps object opacity function to hologram intensity. The first term of the expansion is shown to be equivalent to conventional (optical) reconstruction, with successive terms increasingly sup-pressing the twin image. The algorithm is computationally efficient, requiring only a single fast Fourier transform pair.
262 citations
TL;DR: A very fast deconvolution method, which is based on the fast Fourier transform, can be used to control the outputs from a multichannel plant comprising any number of control sources and error sensors, resulting in a matrix of causal finite impulse response filters whose performance is optimized at a large number of discrete frequencies.
Abstract: A very fast deconvolution method, which is based on the fast Fourier transform (FFT), can be used to control the outputs from a multichannel plant comprising any number of control sources and error sensors. The result is a matrix of causal finite impulse response filters whose performance is optimized at a large number of discrete frequencies. The paper is particularly aimed at multichannel sound reproduction and more specifically reproducing the sound field from a set of loudspeakers.
262 citations
TL;DR: Based on the (m, N, q)-regular Fourier matrix, a new algorithm is proposed for fast Fourier transform (FFT) of nonuniform (unequally spaced) data with accuracy much better than previously reported results with the same computation complexity.
Abstract: Based on the (m, N, q)-regular Fourier matrix, a new algorithm is proposed for fast Fourier transform (FFT) of nonuniform (unequally spaced) data. Numerical results show that the accuracy of this algorithm is much better than previously reported results with the same computation complexity of O(N log/sub 2/ N). Numerical examples are shown for the applications in computational electromagnetics.
11 May 1998
TL;DR: By exploiting the spatial regularity of the new algorithm, minimal requirement for both dominant components in VLSI implementation has been achieved: only 4 complex multipliers and 1024 complex-word data memory for the pipelined 1K FFT processor.
Abstract: The design and implementation of a 1024-point pipeline FFT processor is presented. The architecture is based on a new form of FFT, the radix-2/sup 2/ algorithm. By exploiting the spatial regularity of the new algorithm, minimal requirement for both dominant components in VLSI implementation has been achieved: only 4 complex multipliers and 1024 complex-word data memory for the pipelined 1K FFT processor. The chip has been implement in 0.5 /spl mu/m CMOS technology and takes an area of 40 mm/sup 2/. With 3.3 V power supply, it can compute 2/sup n/, n=0, 1, ..., 10 complex point forward and inverse FFT in real time with up to 30 MHz sampling frequency. The SQNR is above 50 dB for white noise input.
TL;DR: Design algorithms for hybrid filter banks (HFBs) for high-speed, high-resolution conversion between analog and digital signals are presented and a gain normalization technique is developed to maximize the dynamic range in the finite-precision implementation.
Abstract: This paper presents design algorithms for hybrid filter banks (HFBs) for high-speed, high-resolution conversion between analog and digital signals. The HFB is an unconventional class of filter bank that employs both analog and digital filters. When used in conjunction with an array of slower speed converters, the HFB improves the speed and resolution of the conversion compared with the standard time-interleaved array conversion technique. The analog and digital filters in the HFB must be designed so that they adequately isolate the channels and do not introduce reconstruction errors that limit the resolution of the system. To design continuous-time analog filters for HFBs, a discrete-time-to-continuous-time ("Z-to-S") transform is developed to convert a perfect reconstruction (PR) discrete-time filter bank into a near-PR HFB; a computationally efficient algorithm based on the fast Fourier transform (FFT) is developed to design the digital filters for HFBs. A two-channel HFB is designed with sixth-order continuous-time analog filters and length 64 FIR digital filters that yield -86 dB average aliasing error. To design discrete-time analog filters (e.g., switched-capacitors or charge-coupled devices) for HFBs, a lossless factorization of a PR discrete-time filter bank is used so that the reconstruction error is not affected by filter coefficient quantization. A gain normalization technique is developed to maximize the dynamic range in the finite-precision implementation. A four-channel HFB is designed with 9-bit (integer) filter coefficients. With internal precision limited to the equivalent of 15 bits, the maximum aliasing error is -70 dB, and with the equivalent of 20 bits internal precision, maximum aliasing is -100 dB. The 9-bit filter coefficients degrade the stopband attenuation (compared with unquantized coefficients) by less than 3 dB.
TL;DR: A new, faster algorithm for the key step in the HMM calculation employs a fast Fourier transform on the group of pedigree inheritance patterns, which substantially improves the overall performance of the software package GENEHUNTER for performing linkage analysis.
Abstract: Genetic linkage analysis of human pedigrees using many linked markers simultaneously is a difficult computational problem. We have previously described an approach to this problem that uses hidden Markov models (HMMs) and is quite efficient for pedigrees of moderate size. Here, we describe a new, faster algorithm for the key step in the HMM calculation. The algorithm employs a fast Fourier transform on the group of pedigree inheritance patterns. It substantially improves the overall performance of the software package GENEHUNTER for performing linkage analysis. The Fourier representation opens up new research directions for pedigree analysis.
TL;DR: This paper reviews some novel spectral analysis techniques that are useful for neurological signals in general and EEG signals in particular and presents an auto-regressive (AR) modeling based spectral estimation procedure to overcome the problems of lower resolution and 'leakage' effects inherent in the FFT algorithm.
TL;DR: In this paper, a fast and accurate numerical method for free-space beam propagation between arbitrarily oriented planes is developed, which is based on evaluating the Rayleigh-Sommerfeld diffraction integral by use of the fast Fourier transform with a special transformation to handle tilts and offsets of planes.
Abstract: A fast and accurate numerical method for free-space beam propagation between arbitrarily oriented planes is developed. The only approximation made in the development of the method was that the vector nature of light was ignored. The method is based on evaluating the Rayleigh–Sommerfeld diffraction integral by use of the fast Fourier transform with a special transformation to handle tilts and offsets of planes. The fundamental aspects of a software package based on the developed method are presented. A numerical example realized with the software package is presented to establish the validity of the method.
15 Aug 1998-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, the fundamental role of entanglement as the essential nonclassical feature providing the computational speedup in known quantum algorithms is discussed, and the construction of the Fourier...
Abstract: We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speedup in the known quantum algorithms. We review the construction of the Fourier ...
TL;DR: A general efficient method for the fast evaluation of trigonometric polynomials at nonequispaced nodes based on the approximation of the poynomials by special linear combinations of translates of suitable functions ϕ is proposed.
Abstract: In this paper, we are concerned with fast Fourier transforms for nonequispaced grids. We propose a general efficient method for the fast evaluation of trigonometric polynomials at nonequispaced nodes based on the approximation of the polynomials by special linear combinations of translates of suitable functions ϕ. We derive estimates for the approximation error. In particular, we improve the estimates given by Dutt and Rokhlin [7]. As a practical consequence, we obtain a criterion for the choice of the parameters involved in the fast transforms.
TL;DR: In this article, the authors derived a different detection scheme exploiting the assumption that the clutter is wide-sense stationary and demonstrated that the estimation of the structure of the clutter covariance matrix can be reduced to the eigenvalues, which can be (efficiently) done via fast Fourier transform codes.
Abstract: Radar detection of coherent pulse trains embedded in compound-Gaussian disturbance with partially known statistics is discussed. We first give a thorough derivation of two recently proposed adaptive detection structures. Next, we derive a different detection scheme exploiting the assumption that the clutter is wide-sense stationary. Resorting to the theory of circulant matrices, in fact, we demonstrate that the estimation of the structure of the clutter covariance matrix can be reduced to the estimation of its eigenvalues, which in turn can be (efficiently) done via fast Fourier transform codes. After a thorough performance assessment, mostly carried on via computer simulations, the results show that the newly proposed detector achieves better performance than the two previously introduced adaptive detectors. Moreover, a sensitivity analysis shows that, even though this detector does not strictly guarantee the constant false alarm rate property with respect to the clutter covariance matrix, it is robust, in the sense that its performance is only slightly affected by variations in the clutter temporal correlation.
TL;DR: Several algorithms for efficiently evaluating trigonometric polynomials at irregularly spaced points are presented and analyzed and they are compared with regard to their accuracy and their computational efficiency.
Abstract: Several algorithms for efficiently evaluating trigonometric polynomials at irregularly spaced points are presented and analyzed. The algorithms can be viewed as approximate generalizations of the fast Fourier transform (FFT), and they are compared with regard to their accuracy and their computational efficiency.
Patent•
29 Dec 1998TL;DR: In this paper, a method and an apparatus for registering frames of imaging data using Fourier phase matching is presented. But the method is not suitable for the automatic registration of image frames.
Abstract: A method and an apparatus for registering frames of imaging data using Fourier phase matching. Successive image frames of pixel data are processed using an image registration algorithm. Either image frames or the frames after edge detection are transformed into polar-logarithmic coordinates in the frequency domain and the phases of the Fourier transform of the resulting image representations, after inverse Fast Fourier transformation, are matched. The coordinates at the maximum phase difference are used to determine the scaling and rotation parameters needed for image frame registration. The frequency domain representation of one of the image frames is then scaled and rotated using an anti-aliasing algorithm in accordance with those parameters. The phase of the result is matched with the phase of the frequency domain representation of the other image frame to determine the translation parameters needed for image frame registration.
TL;DR: A fast full-wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented, demonstrating the accuracy, efficiency, and capability of this technique.
Abstract: A fast full-wave analysis technique that can be used to analyze the scattering and radiation from large finite arrays of microstrip antennas is presented. The technique discretizes the mixed potential integral equation (MPIE) in the spatial domain by means of a full-wave discrete complex image method. The del operators on the Green's functions are transferred from the singular kernel to the expansion and testing functions. The resultant system of equations is solved using the biconjugate gradient (BCG) method in which the matrix-vector product is evaluated efficiently using the fast Fourier transform (FFT). This results in an efficient and accurate computation of the scattering and radiation from finite arrays of microstrip antennas. Several numerical results are presented, demonstrating the accuracy, efficiency, and capability of this technique.
13 Sep 1998
TL;DR: A new VLSI-oriented fast Fourier transform (FFT) algorithm-radix-2/4/8, which can effectively minimize the number of complex multiplications and is designed for use in the DVB application in 0.3 V triple-metal CMOS process.
Abstract: In this paper, we present a new VLSI-oriented fast Fourier transform (FFT) algorithm-radix-2/4/8, which can effectively minimize the number of complex multiplications. This algorithm can be implemented efficiently using a pipelined architecture. Based on this pipelined architecture, an 8 K FFT ASIC is designed for use in the DVB (Digital Video Broadcasting) application in 0.6 /spl mu/m-3.3 V triple-metal CMOS process.
TL;DR: In this article, an efficient method for analyzing cavity structures by using the fast Fourier transform (FFT)/Pade technique, in combination with the finite-difference time-domain (FDTD) method, is presented.
Abstract: An efficient method for analyzing cavity structures by using the fast Fourier transform (FFT)/Pade technique, in combination with the finite-difference time-domain (FDTD) method, is presented. Without sacrificing the accuracy of the results, this new method significantly reduces the computational time compared to that needed where the conventional FFT algorithm is used. The usefulness of this approach is demonstrated by modeling a lossy cavity and computing its resonant frequencies as well as Q.
TL;DR: A frequency-domain analysis of the expectation-maximization algorithm for maximum-likelihood image estimation that shows how the algorithm achieves this band extrapolation and gives the theoretical absolute bandwidth of the restored image.
Abstract: Computational optical-sectioning microscopy with a nonconfocal microscope is fundamentally limited because the optical transfer function, the Fourier transform of the point-spread function, is exactly zero over a conic region of the spatial-frequency domain. Because of this missing cone of optical information, images are potentially artifactual. To overcome this limitation, superresolution, in the sense of band extrapolation, is necessary. I present a frequency-domain analysis of the expectation-maximization algorithm for maximum-likelihood image estimation that shows how the algorithm achieves this band extrapolation. This analysis gives the theoretical absolute bandwidth of the restored image; however, this absolute value may not be realistic in many cases. Then a second analysis is presented that assumes a Gaussian point-spread function and a specimen function and shows more realistic behavior of the algorithm and demonstrates some of its properties. Experimental results on the superresolving capability of the algorithm are also presented.
TL;DR: A technique based on the combination of Fourier pseudospectral method and the perfectly matched layer (PML) and an FFT (fast Fourier transform) algorithm is developed to simulate transient acoustic wave propagation in multidimensional, inhomogeneous, absorptive media.
Abstract: A technique based on the combination of Fourier pseudospectral method and the perfectly matched layer (PML) is developed to simulate transient acoustic wave propagation in multidimensional, inhomogeneous, absorptive media. Instead of the finite difference approximation in the conventional finite-difference time-domain (FDTD) method, this technique uses trigonometric functions, through an FFT (fast Fourier transform) algorithm, to represent the spatial derivatives in partial differential equations. Traditionally the Fourier pseudospectral method is used only for spatially periodic problems because the use of FFT implies periodicity. In order to overcome this limitation, the perfectly matched layer is used to attenuate the waves from other periods, thus allowing the method to be applicable to unbounded media. This new algorithm, referred to as the pseudospectral time-domain (PSTD) algorithm, is developed to solve large-scale problems for acoustic waves. It has an infinite order of accuracy in the spatial derivatives, and thus requires much fewer unknowns than the conventional FDTD method. Numerical results confirms the efficacy of the PSTD method.
TL;DR: The fast Fourier transform and the maximum entropy method (MEM) have been employed for the analysis of electrochemical noise in corrosion studies, and claims have been made concerning the superiority of one method with respect to another.
Abstract: The fast Fourier transform and the maximum entropy method (MEM) provide algorithms for the estimation of the power spectral density (PSD) of fluctuations Both have been employed for the analysis of electrochemical noise in corrosion studies, and claims have been made concerning the superiority of one method with respect to the other In this paper, the two methods are compared to assess their relative advantages A summary of the principles of the MEM is given and its main properties investigated In particular, the effect on spectrum accuracy of varying the number of coefficients in computing the MEM and the validity of the low-frequency plateau in the PSD usually produced by this technique are examined Also, the robustness of the two methods is compared when the random process is not completely stable, for instance, in the presence of signal drifts or slowly varying amplitude of the fluctuations The results presented may be used as a guideline to choose the best computation method as a function of the measurement conditions
TL;DR: An approximate singular value decomposition (SVD) is proposed, which can be used in a variety of applications and is demonstrated that the approximate SVD can be an effective preconditioner for iterative methods.
TL;DR: Results for a Berea sandstone sample show that the mean pore size distribution, obtained taking several serial cross-sections of the reconstructed 3D porous structure into account, is in good agreement with the original thresholded 2D image.