Fourier series
E482288
A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Fourier series canonical | 7 |
| Fourier series expansions | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4927343 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fourier series Context triple: [Weierstrass M-test, relatedTo, Fourier series]
-
A.
Fourier analysis
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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B.
Fourier
Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
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C.
Fourier inversion theorem
The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
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D.
FFT
FFT is the ICAO airline designator used in aviation to identify Frontier Airlines in flight plans and air traffic control communications.
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E.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Fourier series Target entity description: A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
-
A.
Fourier analysis
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.
-
B.
Fourier
Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
-
C.
Fourier inversion theorem
The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
-
D.
FFT
FFT is the ICAO airline designator used in aviation to identify Frontier Airlines in flight plans and air traffic control communications.
-
E.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
representation of periodic functions ⓘ series expansion ⓘ |
| appliesTo |
piecewise smooth functions
ⓘ
square-integrable periodic functions ⓘ |
| assumesProperty | periodicity of function ⓘ |
| basisProperty | orthogonality of sines and cosines ⓘ |
| convergesInSense |
L2 norm
ⓘ
mean square ⓘ pointwise almost everywhere ⓘ |
| convergesUnderCondition | Dirichlet conditions NERFINISHED ⓘ |
| expandsInDomain |
interval [0,2π]
ⓘ
interval [−π,π] ⓘ |
| field |
Fourier analysis
ⓘ
harmonic analysis ⓘ mathematical analysis ⓘ signal processing ⓘ |
| generalizesTo |
Fourier series on groups
ⓘ
Fourier transform NERFINISHED ⓘ discrete-time Fourier series ⓘ |
| hasComponent |
Fourier coefficients
ⓘ
Fourier cosine series NERFINISHED ⓘ Fourier sine series NERFINISHED ⓘ complex Fourier series ⓘ |
| hasFormulaType |
complex Fourier series
ⓘ
real Fourier series ⓘ |
| introducedBy | Joseph Fourier NERFINISHED ⓘ |
| introducedInWork | Théorie analytique de la chaleur NERFINISHED ⓘ |
| introducedInYear | 1822 ⓘ |
| namedAfter | Joseph Fourier NERFINISHED ⓘ |
| relatedConcept |
Fourier coefficients
ⓘ
Gibbs phenomenon NERFINISHED ⓘ Hilbert space NERFINISHED ⓘ Parseval's identity NERFINISHED ⓘ Plancherel theorem NERFINISHED ⓘ orthogonal functions ⓘ trigonometric polynomials ⓘ |
| represents | periodic function ⓘ |
| usedFor |
acoustics
ⓘ
filter design ⓘ heat equation ⓘ image processing ⓘ quantum mechanics NERFINISHED ⓘ signal decomposition ⓘ solving partial differential equations ⓘ spectral analysis ⓘ vibration analysis ⓘ wave equation ⓘ |
| usesBasisFunctions |
complex exponentials
ⓘ
cosine functions ⓘ sine functions ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Fourier series Description of subject: A Fourier series is a way of representing a periodic function as an infinite sum of sines and cosines with appropriately chosen coefficients.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Fourier series expansions