Noise Analysis of an Algorithm for Uncertain Frequency Identification
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Bibliographic record
Abstract
This note presents a noise analysis for an algorithm to identify the uncertain frequency of periodic signals or disturbances. This algorithm is based on the time-varying states of an internal model principle controller which can be mapped nonlinearly to the frequency and the magnitude or energy of the periodic signal or disturbance. This note provides an analysis of the 'measurement' of this frequency in the presence of white noise. In the case of an additive white noise, we develop some formulas to calculate the means and variances of the measured difference between the true frequency and nominal frequency for high and low signal-to-noise ratio (SNR). When an integral controller is used to eliminate this difference, we prove that this frequency estimation is unbiased. The formulae to calculate the mean and variance are also given for the output of the integral controller. The simulations verify the validity of approximations used in our noise analysis.
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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