Continuous-time Fourier Transform

URI: https://gptkb.org/entity/Continuous-time_Fourier_Transform
GPTKB entity
Statements (33)
Predicate Object
gptkbp:instanceOf gptkb:transformation
gptkbp:abbreviation CTFT
gptkbp:application communications engineering
image processing
audio analysis
system analysis
gptkbp:category Fourier analysis
integral transforms
gptkbp:domain continuous time
gptkbp:hasUnit radians per second
Hertz (Hz)
https://www.w3.org/2000/01/rdf-schema#label Continuous-time Fourier Transform
gptkbp:introduced gptkb:Jean-Baptiste_Joseph_Fourier
gptkbp:inverse_transform Inverse Continuous-time Fourier Transform
gptkbp:mapType time domain to frequency domain
gptkbp:mathematical_expression X(f) = ∫ x(t) e^{-j2πft} dt
gptkbp:output complex-valued function
gptkbp:property gptkb:Parseval's_theorem
scaling
linearity
convolution
frequency shifting
time shifting
gptkbp:relatedTo gptkb:Laplace_Transform
gptkb:Discrete-time_Fourier_Transform
gptkb:Fourier_Series
gptkbp:used_in gptkb:signal_processing
communications
electrical engineering
gptkbp:variant t (time)
f (frequency)
gptkbp:bfsParent gptkb:Discrete-time_Fourier_Transform
gptkbp:bfsLayer 8