Fourier analysis

E173
area of harmonic analysis branch of mathematics mathematical method

Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.

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All labels observed (9)

Label Occurrences
Fourier analysis canonical 18
Fourier series 13
Fourier transform 7

Statements (50)

Predicate Object
instanceOf area of harmonic analysis ⓘ
branch of mathematics ⓘ
mathematical method ⓘ
application MRI reconstruction ⓘ
audio signal processing ⓘ
crystallography ⓘ
data compression ⓘ
heat equation ⓘ
image reconstruction ⓘ
medical imaging ⓘ
optics ⓘ
radar signal processing ⓘ
signal filtering ⓘ
solution of differential equations ⓘ
spectral analysis ⓘ
vibration analysis ⓘ
wave equation ⓘ
basedOn representation of functions as sums of sinusoids ⓘ
superposition principle ⓘ
field acoustics ⓘ
communications engineering ⓘ
control theory ⓘ
electrical engineering ⓘ
image processing ⓘ
mathematics ⓘ
partial differential equations ⓘ
physics ⓘ
quantum mechanics ⓘ
signal processing ⓘ
goal analyze frequency content of signals ⓘ
decompose functions into sinusoidal components ⓘ
historicalDevelopment 19th century ⓘ
historicalFigure Jean-Baptiste Joseph Fourier ⓘ
namedAfter Jean-Baptiste Joseph Fourier ⓘ
surface form: Joseph Fourier
relatedTo Laplace transform ⓘ
distribution theory ⓘ
harmonic analysis ⓘ
time–frequency analysis ⓘ
wavelet analysis ⓘ
usesConcept Fourier analysis self-linksurface differs ⓘ
surface form: Fourier series

Fourier transform ⓘ
Hilbert spaces ⓘ
L2 spaces ⓘ
convolution ⓘ
discrete Fourier transform ⓘ
fast Fourier transform ⓘ
frequency domain ⓘ
inner product spaces ⓘ
orthogonality of functions ⓘ
time domain ⓘ

Referenced by (44)

Full triples — surface form annotated when it differs from this entity's canonical label.

harmonic analyzer → basedOn → Fourier analysis ⓘ
harmonic analyzer → relatedTo → Fourier analysis ⓘ
this entity surface form: Fourier transform
Fourier analysis → usesConcept → Fourier analysis self-linksurface differs ⓘ
this entity surface form: Fourier series
Jean-Baptiste Joseph Fourier → knownFor → Fourier analysis ⓘ
this entity surface form: Fourier series
Jean-Baptiste Joseph Fourier → knownFor → Fourier analysis ⓘ
Huygens–Fresnel principle → usedIn → Fourier analysis ⓘ
this entity surface form: Fourier optics
Théorie analytique de la chaleur → subject → Fourier analysis ⓘ
this entity surface form: Fourier series
Jean-Baptiste → fieldOfWork → Fourier analysis ⓘ
subject surface form: Jean-Baptiste Joseph Fourier
Jean-Baptiste → knownFor → Fourier analysis ⓘ
subject surface form: Jean-Baptiste Joseph Fourier
this entity surface form: Fourier series
Jean-Baptiste → knownFor → Fourier analysis ⓘ
subject surface form: Jean-Baptiste Joseph Fourier
this entity surface form: Fourier transform
Jean-Baptiste → knownFor → Fourier analysis ⓘ
subject surface form: Jean-Baptiste Joseph Fourier
Jean-Baptiste → notableConcept → Fourier analysis ⓘ
subject surface form: Jean-Baptiste Joseph Fourier
this entity surface form: Fourier series expansion of periodic functions
Jean-Baptiste → notableConcept → Fourier analysis ⓘ
subject surface form: Jean-Baptiste Joseph Fourier
this entity surface form: Fourier transform of functions
Minkowski inequality → usedIn → Fourier analysis ⓘ
Gaussian integral → usedIn → Fourier analysis ⓘ
Riemann–Lebesgue lemma → field → Fourier analysis ⓘ
Riemann–Lebesgue lemma → appliesTo → Fourier analysis ⓘ
this entity surface form: Fourier series
Riemann–Lebesgue lemma → appliesTo → Fourier analysis ⓘ
this entity surface form: Fourier transform
Riemann–Lebesgue lemma → relatedTo → Fourier analysis ⓘ
this entity surface form: Fourier transform
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe → mainTopic → Fourier analysis ⓘ
this entity surface form: Fourier series
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe → mathematicalSubjectClassification → Fourier analysis ⓘ
LSZ reduction formula → usesConcept → Fourier analysis ⓘ
this entity surface form: Fourier transform
Engineering Mathematics → coversTopic → Fourier analysis ⓘ
this entity surface form: Fourier series
Euler’s formula for complex exponentials → usedFor → Fourier analysis ⓘ
this entity surface form: Fourier series
Euler’s formula for complex exponentials → usedFor → Fourier analysis ⓘ
this entity surface form: Fourier transforms
Fourier → knownFor → Fourier analysis ⓘ
subject surface form: Jean-Baptiste Joseph Fourier
this entity surface form: Fourier series
Joseph → knownFor → Fourier analysis ⓘ
subject surface form: Joseph Fourier
Joseph → knownFor → Fourier analysis ⓘ
subject surface form: Joseph Fourier
this entity surface form: Fourier series
Joseph → knownFor → Fourier analysis ⓘ
subject surface form: Joseph Fourier
this entity surface form: Fourier transform
John W. Tukey → knownFor → Fourier analysis ⓘ
this entity surface form: Fast Fourier Transform algorithm
Hölder inequality → usedIn → Fourier analysis ⓘ
Divergent Series → topic → Fourier analysis ⓘ
this entity surface form: Fourier series
Hardy–Littlewood circle method → uses → Fourier analysis ⓘ
this entity surface form: Fourier series
Weierstrass approximation theorem → relatedTo → Fourier analysis ⓘ
this entity surface form: Fourier series
Weyl quantization → usesConcept → Fourier analysis ⓘ
this entity surface form: Fourier transform
Elias Stein → notableWork → Fourier analysis ⓘ
this entity surface form: Fourier Analysis: An Introduction
Laplace operator → usedIn → Fourier analysis ⓘ
The Fourier Integral and Certain of Its Applications → field → Fourier analysis ⓘ
Cauchy principal value → usedIn → Fourier analysis ⓘ
dominated convergence theorem → usedIn → Fourier analysis ⓘ
"Functional Analysis" → developedFrom → Fourier analysis ⓘ
subject surface form: Functional analysis
Cooley–Tukey Fast Fourier Transform algorithm → category → Fourier analysis ⓘ
Young inequality for convolutions → usedIn → Fourier analysis ⓘ
Schauder basis → appearsIn → Fourier analysis ⓘ