Space-time trade-offs on the FFT algorithm

  • Authors:

  • J. Savage;S. Swamy

  • Affiliations:

  • -;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

The performance of the fast Fourier transfmm algorithm is examined under limitations on computational space and time. It is shown that if the algorithm withninputs,nas a power of two, is implemented withStemporary locations whereS=o(n/ log n), then the computation timeTgrows faster thann log n. Furthermore,Tcan grow as fast asn^{2}ifS=S_{min} + O(1)whereS_{min}=l+log_{2}n, the minimum necessary. These results are obtained by deriving tight bounds onTversusSandn.