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186
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 153 (51 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy to use, requiring programs of less than fifty lines. The Fourierseries method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same formula is obtained by using the Fourier series of an associated periodic function constructed by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourierseries method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf's, an appropriate truncation of the infinite series can be determined from the transform based on estimates or bounds. For Laplace transforms, the numerical integration can be made to produce a nearly alternating series, so that the convergence can be accelerated by techniques such as Euler summation. Alternatively, the cdf can be perturbed slightly by convolution smoothing or windowing to produce a truncation error bound independent of the original cdf. Although error bounds can be determined, an effective approach is to use two different methods without elaborate error analysis. For this...
Efficiently Supporting Ad Hoc Queries in Large Datasets of Time Sequences
 In SIGMOD
, 1997
"... Ad hoc querying is difficult on very large datasets, since it is usually not possible to have the entire dataset on disk. While compression can be used to decrease the size of the dataset, compressed data is notoriously difficult to index or access. In this paper we consider a very large dataset com ..."
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Cited by 103 (15 self)
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Ad hoc querying is difficult on very large datasets, since it is usually not possible to have the entire dataset on disk. While compression can be used to decrease the size of the dataset, compressed data is notoriously difficult to index or access. In this paper we consider a very large dataset comprising multiple distinct time sequences. Each point in the sequence is a numerical value. We show how to compress such a dataset into a format that supports ad hoc querying, provided that a small error can be tolerated when the data is uncompressed. Experiments on large, real world datasets (AT&T customer calling patterns) show that the proposed method achieves an average of less than 5% error in any data value after compressing to a mere 2.5% of the original space (i.e., a 40:1 compression ratio), with these numbers not very sensitive to dataset size. Experiments on aggregate queries achieved a 0.5% reconstruction error with a space requirement under 2%. 1 Introduction The bulk of the data...
Numerical inversion of probability generating functions
 Oper. Res. Letters
, 1992
"... Random quantities of interest in operations research models can often be determined conveniently in the form of transforms. Hence, numerical transform inversion can be an effective way to obtain desired numerical values of cumulative distribution functions, probability density functions and probabil ..."
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Cited by 43 (17 self)
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Random quantities of interest in operations research models can often be determined conveniently in the form of transforms. Hence, numerical transform inversion can be an effective way to obtain desired numerical values of cumulative distribution functions, probability density functions and probability mass functions. However, numerical transform inversion has not been widely used. This lack of use seems to be due, at least in part, to good simple numerical inversion algorithms not being well known. To help remedy this situation, in this paper we present a version of the Fourierseries method for numerically inverting probability generating functions. We obtain a simple algorithm with a convenient error bound from the discrete Poisson summation formula. The same general approach applies to other transforms. Key Words: numerical inversion of transforms, computational probability, generating functions, Fourierseries method, Poisson summation formula, discrete Fourier transform.
A LowPower, HighPerformance, 1024Point FFT Processor
, 1999
"... This paper presents an energyefficient, singlechip, 1024point fast Fourier transform (FFT) processor. The 460 000transistor design has been fabricated in a standard 0.7 m (Lpoly Lpoly Lpoly =0:6 m) CMOS process and is fully functional on firstpass silicon. At a supply voltage of 1.1 V, it calcul ..."
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Cited by 28 (2 self)
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This paper presents an energyefficient, singlechip, 1024point fast Fourier transform (FFT) processor. The 460 000transistor design has been fabricated in a standard 0.7 m (Lpoly Lpoly Lpoly =0:6 m) CMOS process and is fully functional on firstpass silicon. At a supply voltage of 1.1 V, it calculates a 1024point complex FFT in 330 s while consuming 9.5 mW, resulting in an adjusted energy efficiency more than 16 times greater than the previously most efficient known FFT processor. At 3.3 V, it operates at 173 MHzwhich is a clock rate 2.6 times greater than the previously fastest rate.
Phase Synchronization: From Theory to Data Analysis
, 1999
"... Synchronization of coupled oscillating systems means appearance of certain relations between their phases and frequencies. Here we use this concept in order to address the inverse problem and to reveal interaction between systems from experimental data. We discuss how the phases and frequencies can ..."
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Cited by 21 (5 self)
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Synchronization of coupled oscillating systems means appearance of certain relations between their phases and frequencies. Here we use this concept in order to address the inverse problem and to reveal interaction between systems from experimental data. We discuss how the phases and frequencies can be estimated from time series and present techniques for detection and quantification of synchronization. We apply our approach to human posture control data of healthy subjects and neurological patients, to multichannel magnetoencephalography data and records of muscle activity of a Parkinsonian patient, and also use it to analyse the cardiorespiratory interaction in humans. By means of these examples we demonstrate that our method is effective for the analysis of systems interrelation from noisy nonstationary bivariate data and provides other information than traditional correlation (spectral) techniques. Preprint submitted to Elsevier Preprint 7 December 1999 Contents 1 Introduction 3 1...
Implementation of a 2D Fast Fourier Transform on an FPGABased Custom Computing Machine
 In International Workshop on FieldProgrammable Logic and Applications
, 1995
"... Abstract. The two dimensional fast Fourier transform (2D FFT) is an indispensable operation in many digital signal processing applications but yet is deemed computationally expensive when performed on a conventional general purpose processors. This paper presents the implementation and performance ..."
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Cited by 20 (3 self)
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Abstract. The two dimensional fast Fourier transform (2D FFT) is an indispensable operation in many digital signal processing applications but yet is deemed computationally expensive when performed on a conventional general purpose processors. This paper presents the implementation and performance figures for the Fourier transform on a FPGAbased custom computer. The computation of a 2D FFT requires O(N2 log2N) floating point arithmetic operations for an NxN image. By implementing the FFT algorithm on a custom computing machine (CCM) called Splash2, a computation speed of 180 Mflops and a speedup of 23 times over a Sparc10
The role of preparation in tuning anticipatory and reflex responses during catching
 J Neurosci
, 1989
"... The pattern of muscle responses associated with catching a ball in the presence of vision was investigated by inciependently varying the height of the drop and the mass of the ball. It was found that the anticipatory EMG responses comprised early and late components. The early components were produc ..."
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Cited by 18 (4 self)
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The pattern of muscle responses associated with catching a ball in the presence of vision was investigated by inciependently varying the height of the drop and the mass of the ball. It was found that the anticipatory EMG responses comprised early and late components. The early components were produced at a roughly constant latency (about 130 msec) from the time of ball release. Their mean amplitude decreased with increasing height of fall. Late components represented the major buildup of muscle activity preceding the impact and were accompanied by limb flexion. Their onset time was roughly constant (about 100 msec) with respect to the time of impact (except in wrist extensors). This indicates that the timing of these responses was based on an accurate estimate of the instantaneous values of the timetocontact (time remaining before impact).
Design and implementation of a 1024point pipeline FFT processor
 Proc, IEEECustom Integrated Circuits Conference
, 1998
"... pipeline FFT processor is presented. The architecture is based on a new form of FFT, the radi~2 ~ algorithm. By exploiting the spatial regularity of the new algorithm, minimal requirement for both dominant components in PLSI implementation has been achieved: only 4 complex multipliers and 1024 comp ..."
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Cited by 17 (0 self)
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pipeline FFT processor is presented. The architecture is based on a new form of FFT, the radi~2 ~ algorithm. By exploiting the spatial regularity of the new algorithm, minimal requirement for both dominant components in PLSI implementation has been achieved: only 4 complex multipliers and 1024 complexword data memory for the pipelined 1K FFT processor. The chip has been implement in OSp CMOS technology and takes an area of 40 mm’. With 3.3 ~ power supply, it can compute 2n, n = 0, 1,..., 10 complex point forward and inverse FFT in real time with up to 30MHz sampling frequency. The SQNR is above 50dB for white noise input. I.
Crestfactor minimization using nonlinear chebyshev approximation methods. Instrumentation and Measurement
 IEEE Transactions
, 1991
"... ..."
Probabilistic Arithmetic
, 1989
"... This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to ..."
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Cited by 15 (0 self)
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This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to be able to handle random problems (such as the determination of the distribution of the roots of random algebraic equations) using algorithms which have been developed for the deterministic case. To this end, in this thesis we survey a number of previously proposed methods for calculating convolutions and representing probability distributions and examine their defects. We develop some new results for some of these methods (the Laguerre transform and the histogram method), but ultimately find them unsuitable. We find that the details on how the ordinary convolution equations are calculated are