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List of Fourier analysis topics
Last updated
August 15, 2025
This is a
list of
Fourier analysis
topics
.
Contents
Fourier analysis
Fourier series
Fourier transforms
Discrete Fourier transforms
Applications of Fourier analysis
Algebra and analysis
Harmonic analysis
Harmonic functions
Special functions and generalized functions
Integral transform concepts
Transforms
Integral kernels
Convolution
Analysis of unevenly spaced data
See also
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
Half-range 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
Integral transform
concepts
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
See also
List of cycles
list of Fourier-related transforms
list of harmonic analysis topics
LTI system theory
Autocorrelation
Autocovariance
Whittaker–Shannon interpolation formula
Gabor atom
Marcinkiewicz theorem
Nyquist–Shannon sampling theorem
Riesz–Thorin theorem
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