An algorithm for the machine calculation of complex Fourier series
1965/01/01 by James W. Cooley, J.W. Cooley, John W. Tukey · 12,266 citations
Chemical Engineering · Decision Sciences · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Fourier series #Mathematical analysis #Mathematics #Rheology and Fluid Dynamics Studies #Series (stratigraphy) #Simulation Techniques and Applications
paper · doi:10.1090/s0025-5718-1965-0178586-1
published in Mathematics of Computation 19(90), 297-301 (American Mathematical Society)
openalex publication_date 1965/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract
An efficient method for the calculation of the interactions of a 2m factorial experiment was introduced by Yates and is widely known by his name.The generalization to 3m was given by Box et al. [1].Good [2] generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series.In their full generality, Good's methods are applicable to certain problems in which one must multiply an JV-vector by an JV X N matrix which can be factored into m sparse matrices, where m is proportional to log JV.This results in a procedure requiring a number of operations proportional to JV log JV rather than JV2.These methods are applied here to the calculation of complex Fourier series.They are useful in situations where the number of data points is, or can be chosen to be, a highly composite number.The algorithm is here derived and presented in a rather different form.Attention is given to the choice of JV.It is also shown how special advantage can be obtained in the use of a binary computer with JV = 2m and how the entire calculation can be performed within the array of JV data storage locations used for the given Fourier coefficients.Consider the problem of calculating the complex Fourier series
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- Early Developmental EEG and Seizure Phenotypes in a Full Gene Deletion of Ubiquitin Protein Ligase E3A Rat Model of Angelman Syndrome. [europepmc]
- A Review on Mental Stress Assessment Methods Using EEG Signals. [europepmc]
- Deep learning-based histopathological segmentation for whole slide images of colorectal cancer in a compressed domain. [europepmc]
- Reliability of IMU-Based Gait Assessment in Clinical Stroke Rehabilitation. [europepmc]
- Analysis of Accelerometer and GPS Data for Cattle Behaviour Identification and Anomalous Events Detection. [europepmc]
- Scale-free and oscillatory spectral measures of sleep stages in humans. [europepmc]
- An evolution of low-field strength MRI. [europepmc]
- Data-centric artificial olfactory system based on the eigengraph. [europepmc]
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