# List of Fourier-related transforms

This is a list of linear transformations of functionss related to the Fourier transform. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component.Applied to functions of continuous arguments, Fourier-related transforms include:

- Laplace transform, a related continuous-time transform
- Continuous Fourier transform (often, just
*Fourier transform*or*FT*), with special cases:- Cosine transform and sine transform (for functions of even/odd symmetry)
- Fourier series (for periodic functions)

- Hartley transform
- Short-time Fourier transform (or short-term Fourier transform) (STFT)

- Z-transform, a more general transform of which the DFT is a special case
- Discrete Fourier transform (DFT), with special cases:
- Discrete cosine transform (DCT)
- Discrete sine transform (DST)

- Modified discrete cosine transform (MDCT)
- Discrete Hartley transform (DHT)
- Also the discretized STFT (see above).