Continuous Fourier Transform

URI: https://gptkb.org/entity/Continuous_Fourier_Transform
GPTKB entity
Statements (35)
Predicate Object
gptkbp:instanceOf Mathematical transform
gptkbp:application gptkb:Quantum_mechanics
Image processing
Audio signal analysis
Communications engineering
Spectral analysis
Vibration analysis
gptkbp:category Integral transform
gptkbp:designer gptkb:Inverse_Continuous_Fourier_Transform
gptkbp:field gptkb:Mathematics
gptkb:Physics
gptkb:signal_processing
gptkbp:firstPublished 19th century
gptkbp:form F(ω) = ∫ f(t) e^{-iωt} dt
gptkbp:generalizes Fourier series
gptkbp:hasUnit gptkb:Hertz
https://www.w3.org/2000/01/rdf-schema#label Continuous Fourier Transform
gptkbp:input Continuous-time function
gptkbp:limitation Not suitable for discrete signals
Requires integrable functions
gptkbp:namedAfter gptkb:Joseph_Fourier
gptkbp:output Frequency domain representation
gptkbp:property gptkb:Parseval's_theorem
gptkb:Convolution_theorem
Linearity
Frequency-shifting
Time-shifting
gptkbp:relatedTo gptkb:Laplace_transform
gptkb:Fourier_transform
gptkb:Discrete_Fourier_Transform
gptkbp:usedFor Frequency analysis
gptkbp:variant t (time)
ω (angular frequency)
gptkbp:bfsParent gptkb:Fourier_Transform
gptkbp:bfsLayer 6