This is an alphabetical list of Fourier analysis topics. See also the list of Fourier-related transforms, and the list of harmonic analysis topics.
- Almost periodic function
- ATS theorem
- Autocorrelation
- Autocovariance
- Banach algebra
- Bessel function
- Compact group
- Continuous Fourier transform
- Convergence of Fourier series
- Convolution
- Convolution theorem
- DFT matrix
- Dini test
- Dirichlet kernel
- Dirichlet problem
- Discrete Fourier transform, Discrete Fourier series
- Discrete Hartley transform
- Distribution
- Fast cosine transform
- Fast Fourier transform
- Fejér kernel
- Fourier amplitude sensitivity testing
- Fourier integral operator
- Fourier inversion theorem
- Fourier operator
- Fourier optics
- Fourier series
- Fourier shell correlation
- Fourier transform
- Fourier transform on finite groups
- Fractional Fourier transform
- Frequency spectrum
- Gabor atom
- Generalized Fourier series
- Gibbs phenomenon
- Haar measure
- Hardy space
- Harmonic analysis
- Harmonic function
- Laplace equation
- Laplace operator
- Laplace transform
- List of cycles, a very interdisciplinary article
- List of Fourier-related transforms
- LTI system theory
- Marcinkiewicz theorem
- Modulus of continuity
- Multiplier (Fourier analysis)
- Non-uniform discrete Fourier transform
- Nyquist–Shannon sampling theorem
- oscillatory integral
- oscillatory integral operator
- Paley–Wiener theorem
- Parseval's theorem
- Periodic function
- Peter–Weyl theorem
- Pinsky phenomenon
- Plancherel theorem
- Poisson summation formula
- Pontryagin duality
- Projection-slice theorem
- Regressive discrete Fourier series
- Riesz–Thorin theorem
- Set of uniqueness
- Sigma approximation
- Sine and cosine transforms
- Sobolev space
- Spectrum continuation analysis
- Spherical harmonic
- Standing wave discrete Fourier transform
- Topological group
- Uncertainty principle for the short-time Fourier transform
- Unit circle
- Unit disc
- Whittaker–Shannon interpolation formula
Famous quotes containing the words list of, list and/or analysis:
“Shea—they call him Scholar Jack—
Went down the list of the dead.
Officers, seamen, gunners, marines,
The crews of the gig and yawl,
The bearded man and the lad in his teens,
Carpenters, coal-passers—all.”
—Joseph I. C. Clarke (1846–1925)
“Do your children view themselves as successes or failures? Are they being encouraged to be inquisitive or passive? Are they afraid to challenge authority and to question assumptions? Do they feel comfortable adapting to change? Are they easily discouraged if they cannot arrive at a solution to a problem? The answers to those questions will give you a better appraisal of their education than any list of courses, grades, or test scores.”
—Lawrence Kutner (20th century)
“Analysis as an instrument of enlightenment and civilization is good, in so far as it shatters absurd convictions, acts as a solvent upon natural prejudices, and undermines authority; good, in other words, in that it sets free, refines, humanizes, makes slaves ripe for freedom. But it is bad, very bad, in so far as it stands in the way of action, cannot shape the vital forces, maims life at its roots. Analysis can be a very unappetizing affair, as much so as death.”
—Thomas Mann (1875–1955)