discrete Fourier transform

URI: https://gptkb.org/entity/discrete_Fourier_transform

GPTKB entity

Statements (51)

Predicate	Object
gptkbp:instanceOf	gptkb:transformation
gptkbp:abbreviation	gptkb:DFT
gptkbp:application	data compression image processing audio signal processing spectral analysis solving partial differential equations
gptkbp:basis_functions	complex exponentials
gptkbp:computational_complexity	O(N^2)
gptkbp:designer	inverse discrete Fourier transform
gptkbp:field	gptkb:mathematics gptkb:signal_processing engineering
gptkbp:generalizes	Fourier series
https://www.w3.org/2000/01/rdf-schema#label	discrete Fourier transform
gptkbp:improves	gptkb:fast_Fourier_transform
gptkbp:input	finite sequence of complex numbers time domain signal
gptkbp:introducedIn	1965
gptkbp:inventedBy	gptkb:John_W._Tukey gptkb:James_W._Cooley
gptkbp:mathematical_formula	X_k = Σ_{n=0}^{N-1} x_n * exp(-2πi k n / N)
gptkbp:matrixRepresentation	DFT matrix
gptkbp:output	finite sequence of complex numbers frequency domain representation
gptkbp:property	linear invertible circular convolution convolution theorem applies energy preserving (Parseval's theorem) symmetry properties
gptkbp:purpose	analyze frequency content of signals
gptkbp:recurrence	output is periodic with period N
gptkbp:relatedConcept	gptkb:Laplace_transform gptkb:discrete_cosine_transform gptkb:z-transform gptkb:chirp_z-transform gptkb:Walsh–Hadamard_transform gptkb:short-time_Fourier_transform gptkb:windowed_Fourier_transform
gptkbp:relatedTo	gptkb:Fourier_transform gptkb:fast_Fourier_transform
gptkbp:unitary_form	gptkb:unitary_DFT
gptkbp:used_in	gptkb:radar gptkb:quantum_computing communications seismology digital signal processing medical imaging
gptkbp:bfsParent	gptkb:Fourier_transform
gptkbp:bfsLayer	5