Real-valued fast Fourier transform algorithms
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.
- Publication:
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IEEE Transactions on Acoustics Speech and Signal Processing
- Pub Date:
- June 1987
- DOI:
- Bibcode:
- 1987ITASS..35..849S
- Keywords:
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- Fast Fourier transforms;
- Discrete Fourier transforms;
- Signal processing algorithms;
- Convolutional codes;
- Discrete transforms;
- Application software;
- Algorithm design and analysis;
- NASA;
- Digital images