Hilbert transform
E825432
The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hilbert transform canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T9844044 — 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: Hilbert transform Context triple: [Cauchy principal value, usedIn, Hilbert transform]
-
A.
Fourier transform
The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, widely used in engineering, physics, and signal processing.
-
B.
Laplace transform
The Laplace transform is an integral transform widely used in mathematics, physics, and engineering to convert functions of time into functions of a complex variable, simplifying the analysis and solution of differential equations and linear systems.
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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.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
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E.
Mellin transforms
Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
- 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: Hilbert transform Target entity description: The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
-
A.
Fourier transform
The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, widely used in engineering, physics, and signal processing.
-
B.
Laplace transform
The Laplace transform is an integral transform widely used in mathematics, physics, and engineering to convert functions of time into functions of a complex variable, simplifying the analysis and solution of differential equations and linear systems.
-
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.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
-
E.
Mellin transforms
Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf | integral transform ⓘ |
| actsOn |
L2 function
ⓘ
real-valued function ⓘ tempered distribution ⓘ |
| appliesTo |
spatial signals
ⓘ
time-domain signals ⓘ |
| definition |
(Hf)(x) = (1/π) p.v. ∫_{−∞}^{∞} f(t)/(x−t) dt
ⓘ
principal value convolution with 1/(πt) ⓘ |
| domain |
L2(R)
ⓘ
Lp(R) for 1 < p < ∞ ⓘ |
| field |
Fourier analysis
ⓘ
complex analysis ⓘ harmonic analysis ⓘ signal processing ⓘ |
| FourierMultiplier | −i·sgn(ξ) ⓘ |
| generalization |
discrete-time Hilbert transform
ⓘ
fractional Hilbert transform ⓘ multidimensional Hilbert transform ⓘ
linked to:
Riesz transforms
|
| hasKernel | 1/(πt) ⓘ |
| inverseOf | negative Hilbert transform ⓘ |
| namedAfter | David Hilbert ⓘ |
| produces |
harmonic conjugate
ⓘ
quadrature component of a signal ⓘ |
| property |
Fourier multiplier operator
ⓘ
H^2 = −I on L2(R) modulo constants ⓘ bounded on L2(R) ⓘ convolution operator ⓘ isometry on L2(R) up to a constant factor ⓘ scale invariant ⓘ singular integral operator ⓘ skew-adjoint on L2(R) ⓘ translation invariant ⓘ unitary on L2(R) after suitable normalization ⓘ |
| range |
L2(R)
ⓘ
Lp(R) for 1 < p < ∞ ⓘ |
| relatedConcept |
Bedrosian theorem
ⓘ
Cauchy integral ⓘ
linked to:
Cauchy transform
Hardy spaces ⓘ
linked to:
Hardy space
Kramers–Kronig relations ⓘ Riesz transforms ⓘ analytic signal ⓘ |
| usedFor |
Kramers–Kronig relations
ⓘ
causal filter design ⓘ construction of analytic signal ⓘ dispersion analysis ⓘ envelope detection ⓘ instantaneous frequency estimation ⓘ phase analysis of signals ⓘ |
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: Hilbert transform Description of subject: The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.