Linked from

The 135 pages that link to Fourier transform, each with the reason it gives.

• Parseval's theoremRelated: Its continuous frequency representation gives the integral version of the identity.

• Riemann–Lebesgue lemmaNarrower topic: The lemma describes the Fourier transform’s behavior at large frequencies.

• Spectral analysisRelated: It is the central operation for expressing a signal in the frequency domain.

• Wave vectorRelated: Its spatial-frequency variables are commonly represented by wave vectors.

• Aaron KlugRelated: Fourier methods connect electron diffraction patterns to the molecular images Klug analyzed.

• Lévy's continuity theoremNarrower topic: Characteristic functions are Fourier transforms of probability measures, linking the theorem to harmonic analysis.

• Magnitude (mathematics)Related: The magnitudes of Fourier coefficients describe the strength of frequency components.

• Paul LauterburRelated: Fourier analysis converts spatially encoded NMR signals into images.

• Peter MansfieldRelated: Mansfield’s image reconstruction methods used Fourier analysis to convert measured signals into spatial images.

• Pontryagin dualityRelated: Pontryagin duality provides the group-theoretic setting for Fourier transforms.

• Wave packetRelated: It links a packet’s spatial shape to its spectrum of components.

• Wiener–Khinchin theoremRelated: It converts the autocorrelation function into the power spectrum.

• Bochner's theoremRelated: The theorem states that the positive-definite function is the transform of a measure.

• Even and odd functionsRelated: Parity can make a Fourier transform real, imaginary, or reducible to a cosine or sine transform.

• Imaginary numberRelated: Its complex exponentials combine sine and cosine information.

• Operator theoryRelated: It converts differential operations into multiplication and is studied as an operator on function spaces.

• Rectangular functionRelated: A rectangular pulse transforms to a scaled sinc-shaped spectrum.

• Selberg trace formulaRelated: A transform of the test function connects the formula’s spectral weights to its geometric terms.

• Astronomical interferometerRelated: Interferometric measurements sample spatial frequencies that can be transformed into an image.

• Filter (signal processing)Related: It makes frequency-selective filtering explicit by expressing a signal’s spectral components.

• Gauss circle problemRelated: Transforming the disk's indicator function makes the count accessible to harmonic analysis.

• Herbert A. HauptmanRelated: Crystallographers use Fourier synthesis to convert structure factors into electron-density maps.

• Hilbert transformRelated: In frequency space, the Hilbert transform is multiplication by a simple sign-dependent phase factor.

• Phragmén–Lindelöf principleRelated: Complex growth estimates can constrain Fourier transforms and their inverses.

• Richard R. ErnstRelated: It converts Ernst’s recorded time-domain NMR signals into interpretable frequency spectra.

• Agmon's inequalityRelated: Frequency-space proofs relate derivative norms to weighted Fourier amplitudes.

• Closed-orbit theoryRelated: Transforming spectral oscillations exposes peaks associated with classical return times or actions.

• Delta potentialRelated: In momentum space, a point interaction couples wave components with a constant amplitude.

• Fuglede's conjectureRelated: It converts inner products of exponentials on a set into values of the set's Fourier transform.

• Maryna ViazovskaRelated: Fourier-analytic constraints are central to the auxiliary functions used in the proof.

• Mathematical conceptsRelated: It reveals structure in signals and solves problems across analysis and engineering.

• Mathematical methods in physicsRelated: It converts differential problems into simpler algebraic relations in frequency space.

• Mechanical spectroscopyRelated: Frequency-domain response is related to time-domain material behavior through this transformation.

• Peetre's inequalityRelated: The estimate commonly compares polynomial weights of interacting Fourier frequencies.

• Position and momentum spacesRelated: It converts the position-space wavefunction into the momentum-space wavefunction.