Fast RLS Fourier analyzers in the presence of frequency mismatch
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Bibliographic record
Abstract
Adaptive Fourier analyzers are used to estimate the coefficients of the sine and cosine terms of a noisy sinusoidal signal assuming the frequencies are known. The recursive least square (RLS) Fourier analyzer is a powerful algorithm that provides excellent performance. However, it is computationally very intensive. Furthermore, in real-life applications, the signal frequencies may differ from their assumed or supposed values. This difference, referred to as frequency mismatch (FM), may significantly deteriorate the performance of the RLS. In this paper, we first propose two fast RLS (FRLS) algorithms by utilizing the inherent characteristics of the estimation problem. The new FRLS algorithms perform almost the same as the RLS, while require considerably less computations. Next, the RLS as well as the proposed two FRLS algorithms are modified by incorporating a new adaptive scheme that alleviates the influence of the FM. Extensive simulations are provided to clarify our claims on the proposed FRLS algorithms, and to show that all the modified Fourier analyzers are capable of accommodating the FM very effectively.
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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 | 0.000 |
| 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