Algorithm

Discrete Fourier series

Operand

Fast Fourier transform

Aliasing

Computer science

Fractional Fourier transform

Filter (signal processing)

Fourier series

Discrete-time Fourier transform

Thermodynamics

Physics

Mathematics

Sampling (signal processing)

Fourier analysis

Mathematical analysis

Fourier inversion theorem

Nyquist–Shannon sampling theorem

Discrete Fourier transform (general)

Sample (material)

Cyclotomic fast Fourier transform

Fourier transform

Computer vision

Arithmetic

IEEE Transactions on Education

The advent of the fast Fourier transform method has greatly extended our ability to implement Fourier methods on digital computers. A description of the alogorithm and its programming is given here and followed by a theorem relating its operands, the finite sample sequences, to the continuous functions they often are intended to approximate. An analysis of the error due to discrete sampling over finite ranges is given in terms of aliasing. Procedures for computing Fourier integrals, convolutions and lagged products are outlined.

The Fast Fourier Transform and Its Applications