Fast fourier transform processors using Gaussian residue arithmetic

Journal Article · Thu Aug 01 00:00:00 EDT 1985 · J. Parallel Distrib. Comput.; (United States)

DOI:https://doi.org/10.1016/0743-7315(85)90025-5· OSTI ID:6594506

Despain, A M; Peterson, A M; Rothaus, O S; Wold, E H

Residue arithmetic using moduli which are Gaussian primes is suggested as a method for computing the fast Fourier transform (FFT). For complex operations, a substantial savings in hardware and time over residue arithmetic using real moduli can be obtained using complex moduli. Gaussian residue arithmetic is discussed and methods for conversion into and out of the complex residue representation are developed. This representation lends itself to table-driven computation, allowing very low latency designs to be developed. A 64-point Cooley-Tukey style processor and a 60-point Rader-Winograd style processor using this technique are described and compared. Hardware savings are realized by approximating the rotations necessary to perform the FFT by small complex integers and by scaling the results of the computation at an intermediate point. It is shown that further hardware reductions can be made by developing custom integrated circuits at the expense of latency.

• Research Organization: Computer Sciences Div., Univ. of California, Berkeley, CA 94720
• OSTI ID: 6594506
• Journal Information: J. Parallel Distrib. Comput.; (United States), Vol. 2:3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ARRAY PROCESSORS
COMPUTER ARCHITECTURE
FOURIER TRANSFORMATION
PARALLEL PROCESSING
SUPERCOMPUTERS
COMPARATIVE EVALUATIONS
GAUSSIAN PROCESSES
INTEGRATED CIRCUITS
SCALING LAWS
COMPUTERS
DIGITAL COMPUTERS
ELECTRONIC CIRCUITS
INTEGRAL TRANSFORMATIONS
MICROELECTRONIC CIRCUITS
PROGRAMMING
TRANSFORMATIONS
990210* - Supercomputers- (1987-1989)
990230 - Mathematics & Mathematical Models- (1987-1989)