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:
Others include the:
Scientific and engineering uses of frequency transforms: