Fourier transform

E577496
mathematical 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.

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All labels observed (3)

Label Occurrences
Fourier transform canonical 10
Discrete Cosine Transform 2
Fourier integral 1

Statements (58)

Predicate Object
instanceOf mathematical transform ⓘ
assumes representation of functions as sums or integrals of sinusoids ⓘ
coreConcept frequency decomposition ⓘ
linear superposition of sinusoids ⓘ
spectral representation ⓘ
domainRequirement typically defined for integrable functions ⓘ
fieldOfUse acoustics ⓘ
applied mathematics ⓘ
communications engineering ⓘ
control theory ⓘ
electrical engineering ⓘ
image processing ⓘ
optics ⓘ
physics ⓘ
probability theory ⓘ
quantum mechanics ⓘ
seismology ⓘ
signal processing ⓘ
statistics ⓘ
vibration analysis ⓘ
hasVariant Fourier cosine transform ⓘ
Fourier series NERFINISHED ⓘ
Fourier sine transform NERFINISHED ⓘ
continuous Fourier transform ⓘ
discrete Fourier transform ⓘ
discrete-time Fourier transform ⓘ
fast Fourier transform NERFINISHED ⓘ
fractional Fourier transform ⓘ
multidimensional Fourier transform ⓘ
short-time Fourier transform ⓘ
historicalDevelopment introduced in the study of heat conduction ⓘ
inverseOperation inverse Fourier transform ⓘ
mapsFrom spatial domain ⓘ
time domain ⓘ
mapsTo frequency domain ⓘ
wavenumber domain ⓘ
namedAfter Joseph Fourier NERFINISHED ⓘ
property Parseval theorem NERFINISHED ⓘ
convolution theorem ⓘ
differentiation in time domain corresponds to multiplication in frequency domain ⓘ
duality ⓘ
frequency-shift property ⓘ
linearity ⓘ
modulation property ⓘ
multiplication in time domain corresponds to convolution in frequency domain ⓘ
scaling property ⓘ
time-shift property ⓘ
relatedConcept Laplace transform NERFINISHED ⓘ
wavelet transform ⓘ
z-transform ⓘ
usedFor filter design ⓘ
image reconstruction ⓘ
pattern recognition ⓘ
signal compression ⓘ
solution of differential equations ⓘ
spectral analysis ⓘ
system identification ⓘ
time-frequency analysis ⓘ

Referenced by (13)

Full triples — surface form annotated when it differs from this entity's canonical label.

Laplace transform → relatedTransform → Fourier transform ⓘ
Extrapolation, Interpolation, and Smoothing of Stationary Time Series → usesConcept → Fourier transform ⓘ
The Fourier Integral and Certain of Its Applications → subject → Fourier transform ⓘ
this entity surface form: Fourier integral
The Fourier Integral and Certain of Its Applications → subject → Fourier transform ⓘ
Wiener–Khinchin theorem → usesTransform → Fourier transform ⓘ
Fourier transform infrared spectroscopy → basedOn → Fourier transform ⓘ
de Bruijn–Newman constant → relatedTo → Fourier transform ⓘ
Fourier inversion theorem → dealsWith → Fourier transform ⓘ
Poisson summation formula → involves → Fourier transform ⓘ
MDCT → basedOn → Fourier transform ⓘ
this entity surface form: Discrete Cosine Transform
MDCT → relatedConcept → Fourier transform ⓘ
this entity surface form: Discrete Cosine Transform
Khinchin's representation theorem → usesConcept → Fourier transform ⓘ
X-ray crystallography → uses → Fourier transform ⓘ