a stochastic roundoff error analysis for the fast fourier

  • A stochastic roundoff error analysis for the fast Fourier

    We study the accuracy of the output of the Fast Fourier Transform by estimating the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication. We compare the results with the corresponding ones for the direct algorithm for the Discrete Fourier

  • A Stochastic Roundoff Error Analysis for the Fast Fourier

    This survey stone presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, and periodic

  • A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE FAST

    A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE FAST FOURIER TRANSFORM DANIELA CALVETTI To the memory of Peter Henrici Abstract. We study the accuracy of the output of the Fast Fourier Transform by estimating the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors

  • (PDF) A stochastic roundoff error analysis for the convolution

    We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for the expected value and the variance of the accompanying

  • A stochastic roundoff error analysis for the convolution

    Oct 01, 1992· We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication. These results are compared with the

  • A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE

    A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE CONVOLUTION DANIELA CALVETTI Abstract. We study the accuracy of an algorithm which computes the convo-lution via Radix-2 fast Fourier transforms. Upper bounds are derived for the the results of a similar type of analysis for the Radix-2 fast Fourier transform [2]. The bounds for the expected

  • AMS :: Mathematics of Computation

    Abstract: We study the accuracy of the output of the Fast Fourier Transform by estimating the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication. We compare the results with the corresponding

  • Worst and Average Case Roundoff Error Analysis for FFT

    This stone presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of fast Fourier transform (FFT) with precomputed twiddle factors and shows the strong influence of precomputation errors on the numerical stability of FFT. Numerical tests confirm the theoretical results.

  • AMS :: Mathematics of Computation

    Advancing research. Creating connections. ISSN 1088-6842(online) ISSN 0025-5718(print)

  • (PDF) Roundoff error analysis of the fast Fourier

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  • Roundoff Error Analysis of the Fast Fourier Transform

    ROUNDOFF ERROR ANALYSIS OF FAST FOURIER TRANSFORM 759 number base of the floating-point computing system, t is the number of base-0 digits in the mantissa of the floating-point number, and at least t + 1 digits are used to accumulate sums. For example, e = 16~5 in short-precision floating-point opera-

  • absolute errors are approximated by the first-order terms

    A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE FAST FOURIER TRANSFORM DANIELA CALVETTI To the memory of Peter Henrici ABSTRACT. We study the accuracy of the output of the Fast Fourier Transform by estimating the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors

  • Daniela Calvetti The Mathematics Genealogy Project

    According to our current on-line database, Daniela Calvetti has 15 students and 15 descendants. We welcome any additional information. If you have additional information or corrections regarding this mathematician, please use the update form.To submit students of this mathematician, please use the new data form, noting this mathematician's MGP ID of 24981

  • LIMITED DYNAMIC RANGE OF SPECTRUM ANALYSIS WE TO

    [141 DSP56000 Digital Signal Processor User's Manual. Motorola Corp. [151 D. C. Rife and C. A. Vincent, "The Use of the Dlscrete Fourier Transform in the Measurement of

  • (PDF) Roundoff error analysis of the fast Fourier

    Academia.edu is a platform for academics to share research papers.

  • Limited dynamic range of spectrum analysis due to roundoff

    A statistical model for roundoff errors is used to predict the output noise of the two common forms of the fast Fourier transform (FFT) algorithm, the decimations in-time and in-frequency.

  • Fast Fourier Transforms Request PDF

    Request PDF Fast Fourier Transforms As shown in Chap. 3, any application of Fourier methods leads to the evaluation of a discrete Fourier transform of length N (DFT(N)).

  • Improved Roundoff Error Analysis for Precomputed Twiddle

    The accurate precomputation of the twiddle factors is necessary in order to perform discrete trigonometric transforms. This stone presents both worst case and average case analysis of roundoff errors occurring in eight precomputation methods of twiddle factors. We are interested in methods with small roundoff errors, low complexity and using only little computer memory.

  • Review on stochastic approach to round-off error analysis

    Dec 01, 1988· N. AbounEtude et Réalisation d'un Logiciel Vectorisé du G.R.G. Avec Estimation de la Précision des Résultats et Implémentation de l'Algorithme Vectoriel

  • ROUNDOFF ERROR ANALYSIS OF THE FAST FOURIER

    ROUNDOFF ERROR ANALYSIS OF THE FAST FOURIER TRANSFORM Abstract. This stone presents an analysis of roundoff errors occurring in the floating-point computation of the fast Fourier transform.UPPer bounds are derived for the ratios of the root-mean-square (RMS) and maximum roundoff errors in the output data to the RMS value of the

  • Roundoff Error Analysis of the Recursive Moving Window

    This stone presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of the recursive moving window discrete Fourier transform (DFT) with precomputed twiddle factors. We show the strong influence of precomputation errors both within the initial fast Fourier transform (FFT) and the recursion on the numerical stability.

  • Fast Fourier Transforms SpringerLink

    Abstract. As shown in Chap. 3, any application of Fourier methods leads to the evaluation of a discrete Fourier transform of length N (DFT(N)).Thus the efficient computation of DFT(N) is very important.Therefore this chapter treats fast Fourier transforms. A fast Fourier transform (FFT) is an algorithm for computing the DFT(N) which needs only a relatively low number of arithmetic

  • Improvement of some bounds on the stability of fast

    Three fast Helmholtz solvers based on the Fast Fourier Transform are studied with respect to their stability. It is proved that they are strongly stable, and that the backward relative errors can grow at most like O(log 2 n)ρ0, where ρ0 is the machine roundoff unit.

  • Error Analysis of Some Operations Involved in the Cooley

    An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 90 (1965), 297--301. Google Scholar; P. Duhamel and M. Vetterli. 1990. Fast Fourier transforms: A tutorial review and a state of the art. Signal Process. 19 (1990), 259--299. Google Scholar; W. Gentleman and G. Sande. 1966. Fast Fourier transforms—For fun and

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