Least square identification of alias components of linear periodically time-varying systems and optimal training signal design
Bibliographic record
Abstract
A least-squares (LS) method for identifying alias components of discrete linear periodically time-varying (LPTV) systems is proposed. The authors apply a periodic input signal to a finite impulse response (FIR)–LPTV system and measure the noise-contaminated output. The output of this LPTV system has the same period as the input when the period of the input signal is a multiple of the period of the LPTV system. The authors show that the input and the output can be related by using the discrete Fourier transform. In the frequency domain, an LS method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR–LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)–LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".