1969/06/01 by J.W. Cooley, Peter Lewis, P. D. Welch · 5 citations
Computer Science · Mathematics · #Algorithm #Artificial intelligence #Circular convolution #Computer science #Convolution (computer science) #Convolution theorem #Cyclotomic fast Fourier transform #Digital Filter Design and Implementation #Discrete Fourier transform (general) #Discrete sine transform #Discrete-time Fourier transform #Fourier analysis #Fourier inversion theorem #Fourier transform #Fourier transform on finite groups #Fractional Fourier transform #Hartley transform #Image and Signal Denoising Methods #Mathematical analysis #Mathematics #Non-uniform discrete Fourier transform #Numerical Methods and Algorithms #Product (mathematics)
paper · doi:10.1109/tau.1969.1162036
openalex publication_date 1969/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
The finite Fourier transform of a finite sequence is defined and its elementary properties are developed. The convolution and term-by-term product operations are defined and their equivalent operations in transform space are given. A discussion of the transforms of stretched and sampled functions leads to a sampling theorem for finite sequences. Finally, these results are used to give a simple derivation of the fast Fourier transform algorithm.