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- Prime-factor_FFT_algorithm abstract "The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N = N1N2 as a two-dimensional N1×N2 DFT, but only for the case where N1 and N2 are relatively prime. These smaller transforms of size N1 and N2 can then be evaluated by applying PFA recursively or by using some other FFT algorithm.PFA should not be confused with the mixed-radix generalization of the popular Cooley–Tukey algorithm, which also subdivides a DFT of size N = N1N2 into smaller transforms of size N1 and N2. The latter algorithm can use any factors (not necessarily relatively prime), but it has the disadvantage that it also requires extra multiplications by roots of unity called twiddle factors, in addition to the smaller transforms. On the other hand, PFA has the disadvantages that it only works for relatively prime factors (e.g. it is useless for power-of-two sizes) and that it requires a more complicated re-indexing of the data based on the Chinese remainder theorem (CRT). Note, however, that PFA can be combined with mixed-radix Cooley–Tukey, with the former factorizing N into relatively prime components and the latter handling repeated factors.PFA is also closely related to the nested Winograd FFT algorithm, where the latter performs the decomposed N1 by N2 transform via more sophisticated two-dimensional convolution techniques. Some older papers therefore also call Winograd's algorithm a PFA FFT.(Although the PFA is distinct from the Cooley–Tukey algorithm, Good's 1958 work on the PFA was cited as inspiration by Cooley and Tukey in their famous 1965 paper, and there was initially some confusion about whether the two algorithms were different. In fact, it was the only prior FFT work cited by them, as they were not then aware of the earlier research by Gauss and others.)".
- Prime-factor_FFT_algorithm wikiPageID "241490".
- Prime-factor_FFT_algorithm wikiPageRevisionID "551191453".
- Prime-factor_FFT_algorithm hasPhotoCollection Prime-factor_FFT_algorithm.
- Prime-factor_FFT_algorithm subject Category:FFT_algorithms.
- Prime-factor_FFT_algorithm type Abstraction100002137.
- Prime-factor_FFT_algorithm type Act100030358.
- Prime-factor_FFT_algorithm type Activity100407535.
- Prime-factor_FFT_algorithm type Algorithm105847438.
- Prime-factor_FFT_algorithm type Event100029378.
- Prime-factor_FFT_algorithm type FFTAlgorithms.
- Prime-factor_FFT_algorithm type Procedure101023820.
- Prime-factor_FFT_algorithm type PsychologicalFeature100023100.
- Prime-factor_FFT_algorithm type Rule105846932.
- Prime-factor_FFT_algorithm type YagoPermanentlyLocatedEntity.
- Prime-factor_FFT_algorithm comment "The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N = N1N2 as a two-dimensional N1×N2 DFT, but only for the case where N1 and N2 are relatively prime.".
- Prime-factor_FFT_algorithm label "Prime-factor FFT algorithm".
- Prime-factor_FFT_algorithm label "互質因子算法".
- Prime-factor_FFT_algorithm sameAs m.01k0zt.
- Prime-factor_FFT_algorithm sameAs Q7243214.
- Prime-factor_FFT_algorithm sameAs Q7243214.
- Prime-factor_FFT_algorithm sameAs Prime-factor_FFT_algorithm.
- Prime-factor_FFT_algorithm wasDerivedFrom Prime-factor_FFT_algorithm?oldid=551191453.
- Prime-factor_FFT_algorithm isPrimaryTopicOf Prime-factor_FFT_algorithm.