An Efficient Algorithm for the Computation of the MultidimensionalDiscrete Fourier Transform

  • Authors:

  • S. Bouguezal;D. Chikouche;A. Khellaf

  • Affiliations:

  • Electronics Institute, University of Batna, 05000 Batna, Algeria;Electronics Institute, University of Sétif, 19000 Sétif, Algeria;Laboratoire Antennes, Université de Rennes I, Av. du Général-Leclerc, 35042 Rennes, France

  • Venue:
  • Multidimensional Systems and Signal Processing
  • Year:
  • 1999

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Abstract

Inthis paper, we propose a new approach for computing multidimensionalCooley-Tukey FFT‘s that is suitable for implementation on a varietyof multiprocessor architectures. Our algorithm is derived inthis paper from a Cooley decimation-in-time algorithm by usingan appropriate indexing process and the tensor product properties.It is proved that the number of multiplications necessary tocompute our proposed algorithm is significantly reduced whilethe number of additions remains almost identical to that of conventionalMultidimensional FFT‘s (MFFT). Comparison results show the powerfulperformance of the proposed MFFT algorithm against the row-columnFFT transform when data dimension M is large. Furthermore, thisalgorithm, presented in a simple matrix form, will be much easierto implement in practice. Connections of the proposed approachwith well-known DFT algorithms are included in this paper andmany variations of the proposed algorithm are also pointed out.