Frequency transform

The factual accuracy of this article is disputed.

A frequency transform is the mapping of functions of a function space on the coefficients of basis functions, where the basis functions must have a locality in the frequency spectrum.

This means: Functions are decomposed into wave-like components (as e.g. cosine, sine or wavelets). The result of the transform are the coefficients of the components (basis functions), i.e. their share in the original function. The transform can be reversed (mostly perfectly or nearly perfectly) summing of the correctly weighted base functions.

Frequency transforms are often used as part of the process of transform coding, but have many other uses, including scientific and engineering analysis.

The most important frequency transforms are:

• Fourier transform
  • of which the cosine transform and sine transform are special cases
• short time Fourier transform (STFT)
• wavelet transform

Others include the:

• Discrete Hartley transform
• Discrete cosine transform
• Discrete sine transform

Scientific and engineering uses of frequency transforms:

• Fourier transform spectroscopy

See also:

• Harmonic analysis