1987/06/01 by H.V. Sorensen, Douglas L. Jones, Michael T. Heideman +1 · 6 citations
Computer Science · #Digital Filter Design and Implementation #Image and Signal Denoising Methods #Numerical Methods and Algorithms
paper · doi:10.1109/tassp.1987.1165220
openalex publication_date 1987/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/19
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.