Publication record · 18.cifr/1965.cooley.fft

An algorithm for the machine calculation of complex Fourier series

v1.0.0

James W. Cooley (IBM Research), John W. Tukey (Princeton University)

RAI18.cifr/1965.cooley.fft

Mathematics of Computation· 1965· doi:10.1090/S0025-5718-1965-0178586-1

An efficient method for the calculation of the interactions of a 2^m factorial experiment was attributed to Yates and is widely known in the statistical literature. This note points out that a very similar algorithm can be applied to the calculation of complex Fourier series. Both are special cases of a general transform that can be defined and computed similarly.

fast Fourier transformFFTdiscrete Fourier transformspectral analysisbutterfly algorithmdivide and conquer

✦ Research context

What this agent contributes to the literature.

Problem solved

Direct DFT computation requires O(N^2) complex multiplications, making it prohibitive for large signals on 1960s hardware and expensive even today for very large N. Scientists and engineers needed spectral decomposition of long signals for seismic, audio, and physical analysis but lacked a fast method. The FFT algorithm solved this by exploiting the periodicity and symmetry of the complex exponential twiddle factors.

Novelty

Cooley and Tukey demonstrated that the DFT of N points can be computed in O(N log N) operations rather than the naive O(N^2) by recursively decomposing the DFT into smaller DFTs via a divide-and-conquer butterfly structure. This reduction made large-scale spectral analysis computationally tractable for the first time and is considered one of the most important algorithms of the 20th century.

Related research

Computing related research...

Canvas contract1-in / 1-out · unpacked into signal legacy ports

Sample data

Loading sample data...

Total calls

This month

Citations

Last called

—

Image digest

sha256:0062cc7c700583d05eedc2e9845633c6fe01a918feaa15c1c700ddf931f07f93

Invoke command

python main.py

Inputs

input:application/json

Outputs

output:application/json

Citation

Loading DOI…

Invoke

CPU compute only

How to get GPU access: Your university, lab, or company can become a CIFR institutional member. Members get GPU-accelerated runs for all their researchers. Contact us

Recent invocations(0)

No invocations yet — be the first to call this agent.