List of Fourier analysis topics

This is a list of Fourier analysis topics. See also the list of Fourier-related transforms, and the list of harmonic analysis topics.

Fourier analysis

 * Multiplier (Fourier analysis)
 * Fourier shell correlation
 * Pinsky phenomenon

Fourier series

 * Generalized Fourier series
 * Regressive discrete Fourier series
 * Gibbs phenomenon
 * Sigma approximation
 * Dini test
 * Poisson summation formula
 * Spectrum continuation analysis
 * Convergence of Fourier series

Fourier transforms

 * List of Fourier-related transforms
 * Fourier transform on finite groups
 * Fractional Fourier transform
 * Continuous Fourier transform
 * Fourier operator
 * Fourier inversion theorem
 * Sine and cosine transforms
 * Parseval's theorem
 * Paley–Wiener theorem
 * Projection-slice theorem
 * Frequency spectrum

Discrete Fourier transforms

 * Discrete Fourier series
 * Non-uniform discrete Fourier transform
 * DFT matrix
 * Entropy influence conjecture
 * Fast cosine transform
 * Fast Fourier transform
 * Cyclotomic fast Fourier transform
 * Sparse Fourier transform

Applications of Fourier analysis

 * Fourier amplitude sensitivity testing
 * Fourier optics
 * Quantum mechanics, for
 * Wavefunctions
 * Uncertainty principle
 * Quantum Fourier transform

Algebra and analysis

 * Periodic function
 * Almost periodic function
 * ATS theorem
 * Modulus of continuity
 * Banach algebra
 * Compact group
 * Haar measure
 * Hardy space
 * Sobolev space
 * Topological group

Harmonic analysis

 * Set of uniqueness
 * Pontryagin duality
 * Plancherel theorem
 * Peter–Weyl theorem
 * Fourier integral operator
 * Oscillatory integral operator

Harmonic functions

 * Laplace operator
 * Laplace equation
 * Dirichlet problem
 * Unit circle
 * Unit disc
 * Spherical harmonic

Special functions and generalized functions

 * Bessel function
 * Dirac delta function
 * Distribution
 * Oscillatory integral

Transforms

 * Laplace transform
 * Discrete Hartley transform
 * List of transforms

Integral kernels

 * Dirichlet kernel
 * Fejér kernel

Convolution

 * Convolution theorem

Analysis of unevenly spaced data

 * Least-squares spectral analysis

Other topics

 * List of cycles
 * LTI system theory
 * Autocorrelation
 * Autocovariance
 * Whittaker–Shannon interpolation formula
 * Gabor atom
 * Marcinkiewicz theorem
 * Nyquist–Shannon sampling theorem
 * Riesz–Thorin theorem