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On the real complexity of a complex DFT

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Abstract

We present a method to construct a theoretically fast algorithm for computing the discrete Fourier transform (DFT) of order N = 2n. We show that the DFT of a complex vector of length N is performed with complexity of 3.76875N log2 N real operations of addition, subtraction, and scalar multiplication.

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References

  1. Blahut, R.E., Fast Algorithms for Digital Signal Processing, Reading: Addison-Wesley, 1985. Translated under the title Bystrye algoritmy tsifrovoi obrabotki signalov, Moscow: Mir, 1989.

    Google Scholar 

  2. Vlasenko, V.A., Lappa, Yu.M., and Yaroslavskii, L.P., Metody sinteza bystrykh algoritmov svertki i spektral’nogo analiza signalov (Methods for Fast Convolution Algorithms Synthesis and Signal Spectral Analysis), Moscow: Nauka, 1990.

    MATH  Google Scholar 

  3. Gashkov, S.B. and Sergeev, I.S., Fast Fourier Transform Algorithms, in Diskrentaya matematika i ee prilozheniya (Discrete Mathematics and Its Applications), vol. V, Moscow: Keldysh Inst. Appl. Math., 2009, pp. 3–23.

    Google Scholar 

  4. Winograd, S., On the Multiplicative Complexity of the Discrete Fourier Transform, Adv. in Math., 1979, vol. 32, no. 2, pp. 83–117.

    Article  MATH  MathSciNet  Google Scholar 

  5. Heideman, M.T., Applications of Multiplicative Complexity Theory to Convolution and the Discrete Fourier Transform, PhD Thesis, Rice Univ., Houston, Texas, 1986.

    Google Scholar 

  6. Johnson, S.F. and Frigo, M., A Modified Split-Radix FFT with Fewer Arithmetic Operations, IEEE Trans. Signal Process., 2007, vol. 55, no. 1, pp. 111–119.

    Article  MathSciNet  Google Scholar 

  7. Lundy, T.J. and van Buskirk, J., A New Matrix Approach to Real FFTs and Convolutions of Length 2k, Computing, 2007, vol. 80, no. 1, pp. 23–45.

    Article  MATH  MathSciNet  Google Scholar 

  8. Haynal, S. and Haynal, H., Generating and Searching Families of FFT Algorithms, J. Satisf. Boolean Model. Comput., 2011, vol. 7, no. 4, pp. 145–187.

    MATH  MathSciNet  Google Scholar 

  9. Zheng, W., Li, K., and Li, K., Scaled Radix-2/8 Algorithm for Efficient Computation of Length-N = 2. DFTs, IEEE Trans. Signal Process., 2014, vol. 62, no. 10, pp. 2492–2503.

    Article  MathSciNet  Google Scholar 

  10. Cooley, J.W. and Tukey, J.W., An Algorithm for the Machine Calculation of Complex Fourier Series, Math. Comp., 1965, vol. 19, no. 90, pp. 297–301.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Federal State Unitary Enterprise “Kvant Scientific Research Institute,”, Moscow, Russia

    I. S. Sergeev

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  1. I. S. Sergeev
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Correspondence to I. S. Sergeev.

Additional information

Supported in part by the Russian Foundation for Basic Research, project no. 17-01-00485a.

Original Russian Text © I.S. Sergeev, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 3, pp. 90–99.

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Sergeev, I.S. On the real complexity of a complex DFT. Probl Inf Transm 53, 284–293 (2017). https://doi.org/10.1134/S0032946017030103

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  • DOI: https://doi.org/10.1134/S0032946017030103

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