A Modified Split-Radix FFT With Fewer Arithmetic Operations

  • Authors:

  • S. G. Johnson;M. Frigo

  • Affiliations:

  • MIT, Cambridge, MA;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2007

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Abstract

Recent results by Van Buskirk have broken the record set by Yavne in 1968 for the lowest exact count of real additions and multiplications to compute a power-of-two discrete Fourier transform (DFT). Here, we present a simple recursive modification of the split-radix algorithm that computes the DFT with asymptotically about 6% fewer operations than Yavne, matching the count achieved by Van Buskirk's program-generation framework. We also discuss the application of our algorithm to real-data and real-symmetric (discrete cosine) transforms, where we are again able to achieve lower arithmetic counts than previously published algorithms