Linked from

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

• DispersionRelated: Dispersion acts differently on the frequency components that make up a pulse.

• Doppler spectroscopyRelated: Spectrometers use dispersive or Fourier methods to resolve wavelength-dependent signals.

• Imaginary unitRelated: Complex exponentials built with i make frequency and phase calculations concise.

• Matter waveRelated: It relates a wave packet's spatial extent to its range of momenta.

• ResidueRelated: Contour integration with residues can evaluate many Fourier transforms and inverse transforms.

• Fourier opticsRelated: It converts an optical field between position and spatial-frequency representations.

• Helmholtz equationRelated: It can convert constant-coefficient Helmholtz problems into algebraic relations in frequency space.

• Integration by partsRelated: Integration by parts transfers derivatives between a function and an exponential kernel, producing frequency factors.

• Small-angle X-ray scatteringRelated: Scattering intensity is related to spatial correlations through Fourier-transform relationships.

• Software-defined radioRelated: It underlies software methods for inspecting spectra and implementing filters.

• Acoustic phoneticsRelated: It underlies many methods for analyzing speech spectra.

• Coherence lengthRelated: Frequency decomposition links a wave’s bandwidth to its coherence distance.

• Fundamental solutionRelated: For constant-coefficient operators, it often converts the fundamental-solution equation into an algebraic relation.

• Scattering theoryRelated: It relates position-space scattering descriptions to momentum-transfer measurements.

• Poisson summation formulaRelated: Transforming the function turns its lattice samples into frequency-space terms.

• Polar formRelated: Its complex-valued outputs are often interpreted by magnitude and phase.

• Terence TaoRelated: Fourier methods are among the main tools in Tao’s harmonic analysis and PDE research.

• AutocorrelationRelated: The Wiener–Khinchin theorem connects autocorrelation with the power spectrum through Fourier transforms.

• Dirac combRelated: The comb transforms into another comb, with spacing set by the reciprocal period.

• Integrable functionRelated: For L¹ functions, its defining integral converges absolutely at every frequency.

• Principal symbolRelated: Replacing derivatives by frequency variables explains the symbol’s algebraic form.

• Spectral musicRelated: It provides a way to analyze the component frequencies that spectral composers use as musical material.

• Bessel's inequalityRelated: Related energy bounds constrain frequency-domain coefficients and transforms.

• Momentum operatorRelated: It converts the position-space derivative into multiplication by momentum in momentum space.

• Martin RyleRelated: Aperture synthesis connects measured interferometer data to sky brightness through Fourier relationships.

• Parseval's identityRelated: Its continuous-frequency version relates a function's energy to the energy of its transform.

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

• 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.

• 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.