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gptkbp:instanceOf
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gptkb:transformation
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gptkbp:application
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gptkb:quantum_physics
communications
image processing
audio signal analysis
|
|
gptkbp:basisFor
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complex exponentials
sine and cosine functions
|
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gptkbp:category
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gptkb:integral
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gptkbp:codomain
|
frequency domain
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gptkbp:continuousVersion
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gptkb:Continuous_Fourier_Transform
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gptkbp:designer
|
Inverse Fourier Transform
|
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gptkbp:discreteVersion
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gptkb:Discrete_Fourier_Transform
|
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gptkbp:domain
|
time domain
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gptkbp:extendsTo
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gptkb:Fractional_Fourier_Transform
gptkb:Short-Time_Fourier_Transform
gptkb:Windowed_Fourier_Transform
|
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gptkbp:fastAlgorithm
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gptkb:Fast_Fourier_Transform
|
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gptkbp:field
|
gptkb:mathematics
gptkb:signal_processing
physics
|
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gptkbp:firstPublished
|
1822
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gptkbp:form
|
linear
invertible
unitary (under certain conditions)
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gptkbp:generalizes
|
Fourier series
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Fourier Transform
|
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gptkbp:input
|
gptkb:software
|
|
gptkbp:limitation
|
not always defined for all functions
requires integrable functions
|
|
gptkbp:namedAfter
|
gptkb:Joseph_Fourier
|
|
gptkbp:notation
|
F(f)(ξ)
∫ f(t) e^{-i2πξt} dt
𝓕{f(t)}
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|
gptkbp:output
|
gptkb:software
|
|
gptkbp:purpose
|
decompose functions into frequencies
|
|
gptkbp:recurrence
|
non-periodic signals
|
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gptkbp:relatedConcept
|
gptkb:Laplace_Transform
gptkb:Z-transform
gptkb:Hilbert_Transform
|
|
gptkbp:supportsAlgorithm
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gptkb:FFT
gptkb:DFT
|
|
gptkbp:usedFor
|
solving differential equations
filter design
spectral analysis
frequency analysis
|
|
gptkbp:usedIn
|
seismology
speech recognition
MRI
radar signal analysis
|
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gptkbp:bfsParent
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gptkb:Signal_Processing
gptkb:Digital_Filters
gptkb:spectrometer
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gptkbp:bfsLayer
|
5
|