Comparative Study of the Filtered-X Lms and Lms Algorithms With Undermodelling Conditions
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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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 | 0.003 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".