The Fast Fourier Transform

URI: https://gptkb.org/entity/The_Fast_Fourier_Transform
GPTKB entity
Statements (51)
Predicate Object
gptkbp:instanceOf gptkb:algorithm
gptkbp:abbreviation gptkb:FFT
gptkbp:category gptkb:Mathematics
Digital signal processing
Computer science
Numerical analysis
gptkbp:computes gptkb:Discrete_Fourier_Transform
gptkbp:enables gptkb:MP3_encoding
gptkb:OFDM_(Orthogonal_Frequency_Division_Multiplexing)
gptkb:JPEG_compression
filter design
audio effects
data compression algorithms
image filtering
seismic data analysis
real-time signal processing
frequency domain analysis
spectrogram computation
MRI image reconstruction
efficient convolution
fast polynomial multiplication
gptkbp:hasVariant gptkb:Bluestein's_FFT
gptkb:Radix-2_FFT
gptkb:Radix-4_FFT
gptkb:Split-radix_FFT
Prime-factor FFT
Winograd FFT
https://www.w3.org/2000/01/rdf-schema#label The Fast Fourier Transform
gptkbp:input complex numbers
gptkbp:introduced gptkb:John_Tukey
gptkb:James_Cooley
gptkbp:introducedIn 1965
gptkbp:output complex numbers
gptkbp:popularAlgorithm gptkb:Cooley-Tukey_algorithm
gptkbp:reducesComplexityFrom O(N^2)
gptkbp:reducesComplexityTo O(N log N)
gptkbp:relatedTo gptkb:Discrete_Fourier_Transform
gptkb:Short-time_Fourier_Transform
gptkb:Wavelet_transform
gptkb:Inverse_Fast_Fourier_Transform
Fourier analysis
gptkbp:usedIn gptkb:radar
gptkb:signal_processing
communications
data compression
image processing
medical imaging
spectral analysis
audio analysis
gptkbp:bfsParent gptkb:Top_Ten_Algorithms_of_the_20th_Century_(SIAM)
gptkbp:bfsLayer 8