Accuracy of the discrete Fourier transform and the fast Fourier transform

SIAM Journal on Scientific Computing

Volumn 17, Issue 5, 1996, Pages 1150-1166

  Schatzman, James C ^a  

^a UNIVERSITY OF WYOMING   (United States)

Author keywords

Discrete Fourier transform (DFT); Fast Fourier transform (FFT)

Indexed keywords

EID: 0012032535     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827593247023     Document Type: Article

References (12)

1. C. S. BURRUS, Index mappings for multidimensional formulation of the DFT convolution, IEEE Trans. Acoustics, Speech, Signal Processing, 25 (1977), pp. 239-42.
2. D. CALVETTI, A stochastic roundoff error analysis for the fast Fourier transform, Math. Comp., 56 (1991), pp. 755-774.
3. C. Y. CHU, The Fast Fourier Transform on Hypercube Parallel Computers, Technical Report 87-882, Dept. of Computer Science, Cornell University, Ithaca, NY, 1987.
4. W. M. GENTLEMAN AND G. SANDE, Fast Fourier transforms - For fun and profit, in 1966 Fall Joint Computer Conference, AFIPS Conf. Proceedings #29, Spartan, Washington, D.C., pp. 563-578.
5. D. GOTTLIEB AND S. A. ORSZAG, Numerical Analysis of Spectral Analysis: Theory and Applications, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1977.
6. N. J. HIGHAM, The accuracy of floating-point summation, SIAM J. Sci. Comput., 14 (1993), pp. 783-799.
7. T. KANEKO AND B. LIU, Accumulation of round-off error in fast Fourier transforms, J. Assoc. Comput. Mach., 17 (1970), pp. 637-654.
8. J. OLIVER, Stable methods for evaluating the points cos(iπ/n), J. Inst. Math. Applic., 16 (1975), pp. 247-257.
9. J. SCHATZMAN, Fast Fourier transform algorithms and complexity of the discrete Fourier transform, Math. Comp., submitted.
10. _, Index mappings for the fast Fourier transform, IEEE Trans. Signal Processing, 44 (1996).
11. C. TEMPERTON, Self-sorting mixed-radix fast Fourier transforms, J. Comput. Phys., 52 (1983), pp. 1-23.
12. C. VAN LOAN, Computational Frameworks for the Fast Fourier Transform, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.