Abstract
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 split-radix FFT, an algorithm that uses fewer operations than any other real-valued power-of-2-length FFT. We also compare the performance of inherently real-valued transform algorithms such as the fast Hartley transform (FHT) and the fast cosine transform (FCT) to real-valued FFT algorithms for the computation of power spectra and cyclic convolutions. Comparisons of these techniques reveal that the alternative techniques always require more additions than a method based on a real-valued FFT algorithm and result in computer code of equal or greater length and complexity.
Original language | English (US) |
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Pages (from-to) | 849-863 |
Number of pages | 15 |
Journal | IEEE Transactions on Acoustics, Speech, and Signal Processing |
Volume | 35 |
Issue number | 6 |
DOIs |
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State | Published - Jun 1987 |
Externally published | Yes |
ASJC Scopus subject areas
- Signal Processing