Design of Least-Squares and Minimax Composite Filters
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Bibliographic record
Abstract
We study a class of composite FIR filters (C-filters), each is composed of a prototype filter and a shaping filter in cascade, where the shaping filter is constructed by cascading several complementary comb filters. In particular, the problems of designing C-filters that are optimal in least-squares, equiripple passband and lease-squares stopband, and minimax sense are formulated, and three algorithms for designing such linear-phase FIR C-filters are proposed. The algorithms are based on an alternating optimization strategy in that the prototype and shaping filters are optimized in separate steps, which are coupled and carried out in a sequential manner to yield a satisfactory design. Design examples are presented to illustrate the algorithms and demonstrate the performance of the C-filters relative to their conventional FIR counterparts.
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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 | 0.001 | 0.001 |
| 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