Cramer-Rao Lower Bound for Harmonic and Subharmonic Estimation
Bibliographic record
Abstract
Recently, Zarowski and Kmpyvnytskyy developed a modified iterative cosinor algorithm (MICA) for the estimation of the parameters of sinusoidal signals with harmonics and subharmonics contaminated by AWGN, and derived the Cramer-Rao lower bound (CRLB) for the estimation of fundamental frequency component of such signals. However, their derivation was based on the assumption that the noise variance is known a priori. This paper presents a new derivation of CRLB bound for the case that the noise variance is unknown. The derivations also include the CRLB bounds for the estimation of harmonic and subharmonic amplitudes, noise variance as well as the SNR of the contaminated signal. Numerical simulation results are given to verify and interpret the derived CRLB bounds, together with the evaluation of estimation performance
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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 | 0.007 | 0.046 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.004 |
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".