Discrete Fourier Transform

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:transformation
gptkbp:abbreviation	gptkb:DFT
gptkbp:application	communications data compression image processing audio signal processing filter design spectral estimation
gptkbp:category	Fourier analysis linear operator unitary transform
gptkbp:computational_complexity	O(N^2)
gptkbp:designer	gptkb:Inverse_Discrete_Fourier_Transform
gptkbp:domain	discrete
gptkbp:field	gptkb:mathematics gptkb:signal_processing engineering
gptkbp:hasWikipediaPage	https://en.wikipedia.org/wiki/Discrete_Fourier_transform
https://www.w3.org/2000/01/rdf-schema#label	Discrete Fourier Transform
gptkbp:improves	gptkb:Fast_Fourier_Transform
gptkbp:input	finite sequence
gptkbp:introduced	gptkb:John_W._Tukey gptkb:James_W._Cooley
gptkbp:introducedIn	1965
gptkbp:mathematical_formula	X_k = \\sum_{n=0}^{N-1} x_n e^{-2\\pi i k n / N}
gptkbp:output	finite sequence
gptkbp:range	discrete
gptkbp:relatedTo	gptkb:Fourier_Transform gptkb:Discrete-time_Fourier_Transform gptkb:Fast_Fourier_Transform
gptkbp:usedFor	spectral analysis frequency analysis
gptkbp:bfsParent	gptkb:MDCT_(Modified_Discrete_Cosine_Transform) gptkb:Fourier_Transform gptkb:Quantum_Fourier_Transform gptkb:Digital_Signal_Processing gptkb:Discrete_Cosine_Transform
gptkbp:bfsLayer	6