Instantaneous fundamental frequency estimation of non‐stationary periodic signals using non‐linear recursive filters
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Bibliographic record
Abstract
This paper presents an algorithm for estimating the instantaneous fundamental frequency of a noisy non‐stationary periodic signal whose components are harmonically related. To this end, the authors’ propose a harmonic state‐space model for the input signal and use it to derive an extended Kalman filter (EKF), an unscented Kalman filter (UKF) and a particle filter (PF). In this model, the input signal is characterised by a time‐varying fundamental frequency and amplitude which is a practical assumption for real‐world periodic signals. In contrast to most of existing methods such as short‐time Fourier transform, the proposed algorithm does not use any windowing technique. Therefore the trade‐off between time and frequency resolutions is less controversial and so can be used for real‐time frequency tracking. It also reveals some fine and continuous variations in signal pitch such as Vibrato and Glissando. Simulation results show that the proposed algorithm performs well even when most of the signal energy is contained in the higher‐order harmonics. The performance of the proposed algorithm using EKF, UKF and PF is also evaluated and the results are compared in diverse conditions.
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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 | 0.002 |
| Open science | 0.001 | 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