A multistage DFT-FFT-CZT approach for accurate efficient analysis of sparsely distributed spectra
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Bibliographic record
Abstract
The FFT is a classical approach to fast spectral analysis and measurement. However, it is not the best choice when high accuracy is desired for signals with a very sparse, unpredictable, wide spectral distribution. This paper describes a multistage algorithm designed for more efficient and very accurate calculation of the spectral components in such cases. The approach taken is to combine the advantages of three algorithms FFT CZT and DFT. The FFT is used for a coarse resolution scan of the entire frequency range. The chirp z transform (CZT) is used with an interpolation technique to find a more precise location of the frequency components. The DFT is used along with a windowing technique to ensure a very accurate computation of magnitude and phase. Accurate phase is very difficult to obtain with traditional approaches. This approach shows that depending on the number and distribution of components, and desired accuracy, the combined algorithm can reduce the computational burden by as much as a factor of ten.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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