Analysis of Optimization Algorithms for Non-Uniform Filter Bank Design
Bibliographic record
Abstract
This paper deals with design algorithms for filter banks based on optimization. The design specifications consist of the perfect reconstruction (PR) and frequency response specifications for finite impulse response (FIR) analysis and synthesis filters. The PR conditions are formulated as a set of linear equations with respect to the analysis filters' coefficients and the synthesis filters' coefficients. Two design algorithms are presented; the first is based on an unconstrained optimization of a performance index, which includes the PR error and the error in the frequency specifications. The second algorithm is formulated as a constrained optimization problem with the PR error as the performance index and the frequency specifications as constraints. The performance of the two algorithms is evaluated and compared using two examples; these examples include a compatible nonuniform filter bank (NUFB) and an incompatible NUFB design. The results show that the two algorithms can achieve almost PR and can meet the frequency response specifications in the compatible NUFB. In the case of the incompatible NUFB, PR is more difficult to be achieved.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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) | 0.004 | 0.001 |
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".