Stochastic Analysis of the Normalized Subband Adaptive Filter Algorithm
Bibliographic record
Abstract
This paper studies the statistical behavior of the normalized subband adaptive filtering (NSAF) algorithm. An accurate statistical model of the NSAF algorithm is obtained. In the derivation, we focus on Gaussian correlated input signals. By assuming that the analysis filter bank is paraunitary and taking into account the full band adaptation mechanism of the NSAF, expressions for the first and the second moments of the adaptive filter weights are derived without invoking the slow adaptation assumption. In the derivations, several hyperelliptic integrals appear. To tackle those integrals induced by Gaussian correlated inputs, we first give a solution by resorting to the adaptive Lobatto quadrature. By invoking the averaging principle, two other approximation methods, the chi-square method and the partial fraction expansion method, are presented to approximate the statistical model as well. Monte Carlo (MC) simulation results corroborate our predictions. The Lobatto quadrature method achieves a good agreement with the MC simulation results, even for a relatively large step size. Compared with the chi-square method and the partial fraction expansion method, the Lobatto quadrature method gives better performance in terms of predicting the mean square error when the length of the adaptive filters is small to medium. The chi-square approximation method and the partial fraction expansion method give a satisfactory performance with a relatively low computational complexity when the filter length is large.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".