discrete Fourier transform (DFT)

URI: https://gptkb.org/entity/discrete_Fourier_transform_(DFT)
GPTKB entity
Statements (32)
Predicate Object
gptkbp:instanceOf gptkb:transformation
gptkbp:application gptkb:radar
communications
data compression
spectroscopy
image processing
audio signal processing
gptkbp:category numerical analysis
digital signal processing
gptkbp:designer gptkb:inverse_discrete_Fourier_transform_(IDFT)
gptkbp:field gptkb:mathematics
gptkb:signal_processing
engineering
gptkbp:firstDescribed gptkb:John_W._Tukey
gptkb:James_W._Cooley
gptkbp:form X_k = Σ_{n=0}^{N-1} x_n * exp(-2πi k n / N)
gptkbp:generalizes Fourier series
https://www.w3.org/2000/01/rdf-schema#label discrete Fourier transform (DFT)
gptkbp:implementedIn gptkb:fast_Fourier_transform_(FFT)
gptkbp:input finite sequence of equally-spaced samples
gptkbp:introducedIn 1965
gptkbp:output sequence of complex numbers
gptkbp:property linear
invertible
periodic
complex-valued
gptkbp:relatedTo gptkb:fast_Fourier_transform_(FFT)
gptkb:Fourier_transform
gptkbp:usedFor spectral analysis
frequency analysis
gptkbp:bfsParent gptkb:fast_Fourier_transform_(FFT)
gptkbp:bfsLayer 5