Lesson plan
Split-radix FFT algorithm
The split-radix FFT is a fast Fourier transform (FFT) algorithm for computing the discrete Fourier transform (DFT), and was first described in an initially little-appreciated paper by R. Yavne (1968)and subsequently rediscovered simultaneously by various authors in 1984. (The name "split radix" was coined by two of these reinventors, [[Pierre Duhamel|P. Duhamel] and H. Hollmann.) In particular, split radix is a variant of the Cooley–Tukey FFT algorithm that uses a blend of radices 2 and 4: it recursively expresses a DFT of length N in terms of one smaller DFT of length N/2 and two smaller DFTs of length N/4. The split-radix FFT, along with its variations, long had the distinction of achieving the lowest published arithmetic operation count (total exact number of required real additions and multiplications) to compute a DFT of power-of-two sizes N. The arithmetic count of the original split-radix algorithm was improved upon in 2004 (with the initial gains made in unpublished work by J. Van Buskirk via hand optimization for N=64 [https://web.archive.org/web/20061130110013/http://home.comcast.net/~kmbtib/), but it turns out that one can still achieve the new lowest count by a modification of split radix (Johnson and Frigo, 2007).…
Article summary
The split-radix FFT is a fast Fourier transform (FFT) algorithm for computing the discrete Fourier transform (DFT), and was first described in an initially little-appreciated paper by R. Yavne (1968)and subsequently rediscovered simultaneously by various authors in 1984. (The name "split radix" was coined by two of these reinventors, [[Pierre Duhamel|P. Duhamel] and H. Hollmann.) In particular, split radix is a variant of the Cooley–Tukey FFT algorithm that uses a blend of radices 2 and 4: it recursively expresses a DFT of length N in terms of one smaller DFT of length N/2 and two smaller DFTs of length N/4. The split-radix FFT, along with its variations, long had the distinction of achieving the lowest published arithmetic operation count (total exact number of required real additions and multiplications) to compute a DFT of power-of-two sizes N. The arithmetic count of the original split-radix algorithm was improved upon in 2004 (with the initial gains made in unpublished work by J. Van Buskirk via hand optimization for N=64 [https://web.archive.org/web/20061130110013/http://home.comcast.net/~kmbtib/), but it turns out that one can still achieve the new lowest count by a modification of split radix (Johnson and Frigo, 2007).…
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Discussion questions
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