Discrete Fourier transform

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:transformation
gptkbp:abbreviation	gptkb:DFT
gptkbp:application	gptkb:radar communications data compression spectroscopy image processing audio signal processing
gptkbp:computational_complexity	O(N^2)
gptkbp:designer	gptkb:Inverse_Discrete_Fourier_Transform
gptkbp:domain	discrete
gptkbp:efficient_algorithm	gptkb:Fast_Fourier_transform
gptkbp:field	gptkb:mathematics gptkb:signal_processing engineering physics
gptkbp:firstPublished	19th century
gptkbp:form	X_k = \\sum_{n=0}^{N-1} x_n e^{-i 2\\pi k n / N}
gptkbp:generalizes	multidimensional DFT non-uniform DFT
gptkbp:hasUnit	gptkb:Hertz radians per sample
https://www.w3.org/2000/01/rdf-schema#label	Discrete Fourier transform
gptkbp:input	finite sequence of equally-spaced samples
gptkbp:introduced	gptkb:Jean_Baptiste_Joseph_Fourier
gptkbp:output	same-length sequence of complex numbers
gptkbp:property	linear invertible periodic complex-valued
gptkbp:range	frequency domain
gptkbp:recurrence	N
gptkbp:relatedTo	gptkb:Fourier_transform gptkb:Z-transform gptkb:Discrete-time_Fourier_transform gptkb:Fast_Fourier_transform
gptkbp:used_in	gptkb:machine_learning cryptography seismology telecommunications pattern recognition medical imaging digital electronics music analysis speech analysis vibration analysis
gptkbp:usedFor	digital signal processing spectral analysis frequency analysis
gptkbp:bfsParent	gptkb:Z-Transform gptkb:Cooley–Tukey_algorithm gptkb:Split-radix_FFT
gptkbp:bfsLayer	6