Fourier transform

mathematical transform that expresses a function of time as a function of frequency

AI overview

The Fourier transform is a mathematical tool that takes a signal or function spread out over time and converts it into a description of what frequencies it contains instead. This is useful because many problems become easier to understand and solve when you look at them in terms of frequencies rather than time.

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Image: Fourier transform time and frequency domains.gif

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Commons category: Fourier transformation
short name: FT
Stack Exchange tag: ai.stackexchange.com/tags/fourier-transform

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Article

The Fourier transform applied to the waveform of a C major piano chord (with logarithmic horizontal (frequency) axis). The first three peaks on the left correspond to the fundamental frequencies of the chord (C, E, G). The remaining smaller peaks are higher-frequency overtones of the fundamental pitches.

In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches.