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This tutorial paper describes the methods for constructing fast algorithms for the computation of the discrete Fourier transform (DFT) of a real-valued series. The application of these ideas to all the major fast Fourier transform (FFT) algorithms is discussed, and the various algorithms are compared. We present a new implementation of the real-valued… (More)

- Michael T. Heideman, Don H. Johnson, Sidney Burrus
- 1985

Introduction The fast FOURIER transform (FFT) has become well known as a very efficient algorithm for calculating the discrete FOURIER transform (D F T)-a formula for evaluating the N FOURIER coefficients from a sequence of N numbers. The DFT is used in many disciplines to obtain the spectrum or frequency content of a signal and to facilitate the… (More)

- D F Elliott, Rao, M T Heideman, D H Johnson, C Burris
- 1998

integer arithmetic modulo some large prime N +1, and the N th root of 1 by the modulo arithmetic equivalent. Strictly speaking, these are not Fourier transforms at all, but the properties are quite similar and computational speed can be far superior. On the other hand, their use is somewhat restricted to quantities like correlations and convolutions since… (More)

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