Discrete Fourier Transform (DFT)

URI: https://gptkb.org/entity/Discrete_Fourier_Transform_(DFT)
GPTKB entity
Statements (41)
Predicate Object
gptkbp:instanceOf gptkb:transformation
gptkbp:abbreviation gptkb:DFT
gptkbp:application data compression
image processing
audio signal processing
filter design
spectral analysis
gptkbp:assumes periodic input signal
gptkbp:basisFor complex exponentials
gptkbp:complexity O(N^2)
gptkbp:designer gptkb:Inverse_Discrete_Fourier_Transform_(IDFT)
gptkbp:developedBy Jean-Baptiste Joseph Fourier (conceptual origin)
gptkbp:domain discrete
gptkbp:field gptkb:mathematics
gptkb:signal_processing
engineering
gptkbp:firstPublished 1965 (FFT algorithm by Cooley and Tukey)
gptkbp:form X_k = sum_{n=0}^{N-1} x_n * exp(-2πi k n / N)
gptkbp:hasUnit frequency bins
https://www.w3.org/2000/01/rdf-schema#label Discrete Fourier Transform (DFT)
gptkbp:improves gptkb:Fast_Fourier_Transform_(FFT)
gptkbp:input finite sequence of complex numbers
gptkbp:limitation gptkb:picket_fence_effect
spectral leakage
computationally intensive for large N
gptkbp:output finite sequence of complex numbers
gptkbp:property linear
invertible
periodic
complex-valued
gptkbp:purpose analyze frequency content of signals
gptkbp:range discrete
gptkbp:relatedTo gptkb:Fourier_Transform
gptkb:Fast_Fourier_Transform_(FFT)
gptkb:Discrete-Time_Fourier_Transform_(DTFT)
gptkbp:usedIn applied mathematics
communications
physics
digital signal processing
gptkbp:bfsParent gptkb:Fast_Fourier_Transform_(FFT)
gptkbp:bfsLayer 5