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.

DOI: 10.1109/TASSP.1987.1165220

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@article{Sorensen1987RealvaluedFF, title={Real-valued fast Fourier transform algorithms}, author={Henrik V. Sorensen and Douglas L. Jones and Michael T. Heideman and C. Sidney Burrus}, journal={IEEE Trans. Acoustics, Speech, and Signal Processing}, year={1987}, volume={35}, pages={849-863} }