New radix-(2/spl times/2/spl times/2)/(4/spl times/4/spl times/4) and radix-(2/spl times/2/spl times/2)/(8/spl times/8/spl times/8) DIF FFT algorithms for 3-D DFT
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Bibliographic record
Abstract
In this paper, new three-dimensional (3-D) radix-(2/spl times/2/spl times/2)/(4/spl times/4/spl times/4) and radix-(2/spl times/2/spl times/2)/(8/spl times/8/spl times/8) decimation-in-frequency (DIF) fast Fourier transform (FFT) algorithms are developed and their implementation schemes discussed. The algorithms are developed by introducing the radix-2/4 and radix-2/8 approaches in the computation of the 3-D DFT using the Kronecker product and appropriate index mappings. The butterflies of the proposed algorithms are characterized by simple closed-form expressions facilitating easy software or hardware implementations of the algorithms. Comparisons between the proposed algorithms and the existing 3-D radix-(2/spl times/2/spl times/2) FFT algorithm are carried out showing that significant savings in terms of the number of arithmetic operations, data transfers, and twiddle factor evaluations or accesses to the lookup table can be achieved using the radix-(2/spl times/2/spl times/2)/(4/spl times/4/spl times/4) DIF FFT algorithm over the radix-(2/spl times/2/spl times/2) FFT algorithm. It is also established that further savings can be achieved by using the radix-(2/spl times/2/spl times/2)/(8/spl times/8/spl times/8) DIF FFT algorithm.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it