List of Fourier analysis topics

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

## Contents

* 1 Fourier analysis
* 1.1 Fourier series
* 1.2 Fourier transforms
* 1.3 Discrete Fourier transforms
* 1.4 Applications of Fourier analysis
* 2 Algebra and analysis
* 2.1 Harmonic analysis
* 2.2 Harmonic functions
* 2.3 Special functions and generalized functions
* 3 Integral transform concepts
* 3.1 Transforms
* 3.2 Integral kernels
* 3.3 Convolution
* 4 Analysis of unevenly spaced data
* 5 Other 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

## 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

## 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

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