Comparative Study of the Filtered-X Lms and Lms Algorithms With Undermodelling Conditions
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Bibliographic record
Abstract
The intentional use of a filtered version of the error in LMS updates has been proposed recently for a number of applications, including psycho-acoustic shaping of the spectrum of residual error in active noise cancellation. This article studies the performance of the filtered-X LMS (FXLMS) algorithm in this type of application compared to the standard LMS algorithm, assuming the general case of undermodelling of the unknown system response, Expressions of the mean coefficient vector and mean squared error are derived, providing insight into the essential factors influencing the relative performance of the FXLMS algorithm. It will be shown that the improved performance of the FXLMS algorithm over the LMS algorithm within the desired frequency range (as is generally expected in the literature) is not guaranteed and is heavily dependent on the combination of the level of undermodellmg, nature of the unknown system response, and nature of the filter used in the FXLMS algorithm to filter the output error. Simulation examples axe presented to substantiate our conclusions.
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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