A Comparative Analysis of Fft Algorithms

With the rapid development of computer technology, general purpose CPUs have made inroads into many signal processing applications; of which the Fast Fourier Transform (FFT) continues to be an integral part. A large number of FFT algorithms have been developed over the years, notably the Radix-2, Radix-4, Split-Radix, Fast Hartley Transform (FHT), Quick Fourier Transform (QFT), and the Decimation-in-Time-Frequency (DITF) algorithms. How these algorithms fare in comparison with each other is of considerable interest to developers of signal processing technology. In previous benchmarking efforts, only the computation speed or the number of mathematical operations were used for assessing efficiency. Moreover, most of these benchmarks have been limited to special purpose CPUs like DSPs. In this paper, we present a rigorous analysis of the aforementioned algorithms on general purpose processors, such as the DEC Alpha, Intel Pentium Pro and Sun UltraSparc. The analysis of each algorithm includes the number of mathematical operations, computation time, memory requirements, and compiler effects. Our work is one of the first efforts to characterize FFT algorithms in terms of memory requirements and detailed operation counts. The results indicate that the FHT is the overall best algorithm on all platforms, offering the fastest execution time and requiring reasonably small amounts of memory. EDICS: SP 2.2.6 CORRESPONDENCE: Aravind Ganapathiraju Institute for Signal and Information Processing Department of Electrical and Computer Engineering, PO Box 9571 Mississippi State University, Mississippi State, MS 39762 Phone: (601) 325-8335 Fax: (601) 325-3149 Email: [email protected] COMPARATIVE ANALYSIS OF FFT ALGORITHMS PAGE 1 OF 24