This is a list of Fourier 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
- 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