An Approach for Computing the Radix-2/4 DIT FHT and FFT Algorithms Using a Unified Structure
Bibliographic record
Abstract
By using an appropriate index mapping and by introducing a unified approach for the development of the radix-2/4 decimation-in-time (DIT) fast Hartley transform (FHT) and complex-valued fast Fourier transform (FFT) algorithms, it is shown that there is a close relationship between the structures of the two algorithms. As a result of this close relationship, it is shown that only a single general butterfly is sufficient to implement the two algorithms. This type of relationship is of significant importance for software and hardware implementations of the algorithms, since this relationship, along with the fact that the DHT (discrete Hartley transform) is an efficient alternative to the DFT (discrete Fourier transform) for real data, makes it possible for a single software or hardware module to be used for the computation of the DHT as well as for the computation of the forward and inverse DFTs for real- or complex-valued data.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".