Butterfly diagram

Signal-flow graph connecting the inputs x (left) to the outputs y that depend on them (right) for a

A decimation-in-time radix-2 FFT breaks a length-N DFT into two length-N/2 DFTs followed by a combining stage consisting of many butterfly operations.

This article is about butterfly diagrams in FFT algorithms; for the sunspot diagrams of the same name, see Solar cycle.

In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The earliest occurrence in print of the term is thought to be in a 1969 MIT technical report. The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states.

单词	Butterfly diagram
释义	Butterfly diagram 英语百科 Butterfly diagram This article is about butterfly diagrams in FFT algorithms; for the sunspot diagrams of the same name, see Solar cycle. In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The earliest occurrence in print of the term is thought to be in a 1969 MIT technical report. The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states.
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