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gptkbp:instanceOf
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gptkb:transformation
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gptkbp:application
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acoustics
communications
data compression
quantum mechanics
seismology
spectroscopy
medical imaging
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gptkbp:appliesTo
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signals
functions
distributions
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gptkbp:basisFor
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cosine
sine
complex exponentials
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gptkbp:continuousVersion
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gptkb:continuous_Fourier_transform
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gptkbp:designer
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inverse Fourier transform
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gptkbp:discreteVersion
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gptkb:discrete_Fourier_transform
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gptkbp:domain
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complex numbers
real numbers
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gptkbp:fastAlgorithm
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gptkb:fast_Fourier_transform
|
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gptkbp:field
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gptkb:mathematics
gptkb:signal_processing
physics
|
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gptkbp:firstPublished
|
1822
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gptkbp:generalizes
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Fourier series
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https://www.w3.org/2000/01/rdf-schema#label
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Fourier transform
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gptkbp:mapType
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time domain
frequency domain
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gptkbp:namedAfter
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gptkb:Joseph_Fourier
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gptkbp:notation
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F(f)(ξ)
\\hat{f}(ξ)
\\mathcal{F}\\{f\\}
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gptkbp:property
|
gptkb:convolution_theorem
gptkb:Parseval's_theorem
scaling
linearity
duality
frequency-shifting
time-shifting
|
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gptkbp:range
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complex numbers
real numbers
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gptkbp:relatedTo
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gptkb:Laplace_transform
gptkb:Z-transform
gptkb:Hilbert_transform
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gptkbp:usedFor
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solving differential equations
image processing
audio signal analysis
frequency analysis
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gptkbp:bfsParent
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gptkb:signal_processing
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gptkbp:bfsLayer
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4
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