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Radix 2 FFT

When $ N$ is a power of $ 2$ , say $ N=2^K$ where $ K>1$ is an integer, then the above DIT decomposition can be performed $ K-1$ times, until each DFT is length $ 2$ . A length $ 2$ DFT requires no multiplies. The overall result is called a radix 2 FFT. A different radix 2 FFT is derived by performing decimation in frequency.

A split radix FFT is theoretically more efficient than a pure radix 2 algorithm [76,32] because it minimizes real arithmetic operations. The term ``split radix'' refers to a DIT decomposition that combines portions of one radix 2 and two radix 4 FFTs [23].A.3On modern general-purpose processors, however, computation time is often not minimized by minimizing the arithmetic operation count (see §A.7 below).

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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8
Copyright © 2024-04-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University