List of transforms

This is a list of transforms in mathematics.

Integral transforms

Main article: Integral transform

• Abel transform
• Aboodh transform
• Bateman transform
• Fourier transform
  • Fourier cosine transform
  • Fourier sine transform
  • Fractional Fourier transform
  • Short-time Fourier transform
    • Rectangular mask short-time Fourier transform
  • Fourier–Bros–Iagolnitzer transform
  • Gabor transform
• Hankel transform
• Hartley transform
• Hermite transform
• Hilbert transform
  • Hilbert–Schmidt integral operator
• Jacobi transform
• Laguerre transform
• Laplace transform
  • Inverse Laplace transform
  • Two-sided Laplace transform
  • Inverse two-sided Laplace transform
• Laplace–Carson transform
• Laplace–Stieltjes transform
• Legendre transform
  • Associated Legendre transform
• Linear canonical transform
• Mellin transform
  • Inverse Mellin transform
  • Poisson–Mellin–Newton cycle
• N-transform
• Radon transform
  • X-ray transform
• Shehu transform
• Stieltjes transformation
• Sumudu transform
• Wavelet transform (integral)
• Weierstrass transform

Discrete transforms

Main article: Discrete transform

• Binomial transform
• Discrete Fourier transform, DFT
  • Fast Fourier transform, a popular implementation of the DFT
• Discrete cosine transform
  • Modified discrete cosine transform
• Discrete Hartley transform
• Discrete sine transform
• Discrete wavelet transform
• Hadamard transform (or, Walsh–Hadamard transform)
  • Fast wavelet transform
• Hankel transform, the determinant of the Hankel matrix
• Discrete Chebyshev transform
  • Equivalent, up to a diagonal scaling, to a discrete cosine transform
• Finite Legendre transform
• Irrational base discrete weighted transform
• Mojette transform
• Number-theoretic transform
• Spherical Harmonic transform
• Stirling transform

Discrete-time transforms

These transforms have a continuous frequency domain:

• Discrete-time Fourier transform
• Z-transform

Data-dependent transforms

• Karhunen–Loève transform

Other transforms

• Affine transformation (Euclidean geometry)
• Bäcklund transform
• Bilinear transform
• Box–Muller transform
• Burrows–Wheeler transform (data compression)
• Chirplet transform
• Distance transform
• Fractal transform
• Gelfand transform
• Hadamard transform
• Hough transform (digital image processing)
• Inverse scattering transform
• Legendre transformation
• Möbius transformation
• Perspective transform (computer graphics)
• Sequence transform
• Watershed transform (digital image processing)
• Wavelet transform (orthonormal)
• Y-Δ transform (electrical circuits)

See also

• Linear transform
• List of Fourier-related transforms
• Sequence transformation
• Transform coding
• All pages with titles containing transform

External links

• Tables of Integral Transforms at EqWorld: The World of Mathematical Equations.