Skip to main content
SpringerLink
Log in

Algorithm fast fourier transforms with recursively generated trigonometric functions

Algorithmus 49. Schnelle Fouriertransformation mit rekursiv generierten trigonometrischen Funktionen

  • Algorithm
  • Published:
Computing Aims and scope Submit manuscript

Abstract

New recursive formulae for trigonometric functions generation suitable for FFT algorithms are given. Evaluation of one pair of trigonometric coefficients thus requires 2 multiplications and 2 additions only. Speed comparisons of various radices 2, 4 and 8 FFT FORTRAN realizations were performed. An efficient FORTRAN IV program for one-dimensional complex FFT based on radix 8 algorithm with recursively generated trigonometric coefficients is supplied.

Zusammenfassung

Es werden neue, sich für FFT Algorithmen eignende rekursive Formeln zur Generierung von trigonometrischen Funktionen angegeben. Die Berechnung von einem trigonometrischen Koeffizientenpaar erfordert nur 2 Multiplikationen und 2 Additionen. Die Rechengeschwindigkeiten von verschiedenen Radix-2-,-4- und-8-FFT-FORTRAN-Realisierungen werden verglichen. Ein zeitsparendes, auf dem Radix-8-Algorithmus mit rekursiv generierten trigonometrischen Koeffizienten basiertes FORTRAN IV Programm wird geliefert.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cohran, W. T., et al.: What is the fast Fourier transform? IEEE Trans. Audio Electroacoust.AU-15, 45–55 (1967).

    Google Scholar 

  2. Bergland, G. D.: A fast Fourier transform algorithm using base 8. Math. Comp.22,275–279 (1968).

    Google Scholar 

  3. Singleton, R. C.: A method for computing the fast Fourier transform with auxiliary memory and limited high-speed storage. IEEE Trans. Audio Electroacoust.AU-15, 91–98 (1967).

    Google Scholar 

  4. Singleton, R. C.: An algol convolution procedure based on the fast Fourier transform. Algorithm 345. Commun. ACM12, 179–184 (1969).

    Google Scholar 

  5. Singleton, R. C.: An algorithm for computing the mixed radix fast Fourier transform.IEEE Trans. Audio Electroacoust.AU-17, 83–103 (1969).

    Google Scholar 

  6. Dobeš, K.: Discrete signal processing library, Vol. 1: Fast Fourier transform. Geophysical Institute, Czechoslovak Academy of Sci., Prague, 1977.

    Google Scholar 

  7. Monro, D. M.: Algorithm AS 83. Complex discrete fast Fourier transform. Appl. Statist.24, 268–272 (1975).

    Google Scholar 

  8. System/360 scientific subroutine package (FORTRAN). Version III. IBM Application Program.

  9. Brenner, N.: Cooley — Tukey fast Fourier transform — FOUR2 in assembler language, 360D-13.4.008. Contributed Program Library. IBM Corporation, 1969.

Download references

Author information

Authors and Affiliations

  1. Geophysical Institute, Czechoslovak Academy of Sciences, Bocni II, 141 31, Prague, Czechoslovakia

    K. Dobeš

Authors
  1. K. Dobeš
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dobeš, K. Algorithm fast fourier transforms with recursively generated trigonometric functions. Computing 29, 263–276 (1982). https://doi.org/10.1007/BF02241701

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02241701

Key words

Schlüsselwörter

Search

Navigation