Fourier transform
- Category
- DSP
- Definition
- A layered explanation of the Fourier transform as a change of viewpoint from position to frequency, covering wave matching, phase, inversion and the published Riemann Console Fourier bridge.
- Math Level
- TECHNICAL
- Index Excerpt
- Fourier transform; frequency; phase; spectrum; inversion; wave matching; completed sideband; T2
Fourier transform
The Fourier transform rewrites a function or signal in terms of frequency components rather than its original position- or time-based description.
In one common convention, a function is transformed into a frequency-domain function by integrating against complex oscillations. Different fields use different normalisation constants, but the underlying idea is the same.
Fourier transforms are fundamental in harmonic analysis, signal processing, partial differential equations, probability and mathematical physics.
See also: Fourier analysis, spectral density. .