continuous Fourier transform
GPTKB entity
Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:transformation
|
| gptkbp:application |
communications engineering
quantum mechanics image processing audio signal analysis |
| gptkbp:codomain |
continuous frequency
|
| gptkbp:definedIn |
gptkb:integral
|
| gptkbp:designer |
inverse continuous Fourier transform
|
| gptkbp:domain |
continuous time
|
| gptkbp:field |
gptkb:mathematics
gptkb:signal_processing physics |
| gptkbp:form |
F(ω) = ∫ f(t) e^{-iωt} dt
|
| gptkbp:generalizes |
Fourier series
|
| https://www.w3.org/2000/01/rdf-schema#label |
continuous Fourier transform
|
| gptkbp:introduced |
gptkb:Joseph_Fourier
|
| gptkbp:mapType |
function of time to function of frequency
|
| gptkbp:notation |
F(f)
F(ω) \\hat{f}(\\xi) |
| gptkbp:property |
gptkb:convolution_theorem
gptkb:Parseval's_theorem scaling linearity frequency-shifting time-shifting |
| gptkbp:relatedTo |
gptkb:Laplace_transform
gptkb:Fourier_transform gptkb:discrete_Fourier_transform |
| gptkbp:usedFor |
solving differential equations
frequency analysis |
| gptkbp:bfsParent |
gptkb:Fourier_transform
|
| gptkbp:bfsLayer |
5
|