Nearly Linear-Phase 2-D Recursive Digital Filters Design using
Balanced Realization Model Reduction
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Bibliographic record
Abstract
This paper presents a new method for the design of separable denominators 2-D IIR filters with nearly linear phase in the passband.
 The design method is based on a balanced-realization model reduction technique.
 The nearly linear-phase 2-D IIR filter is designed using 2-D model reduction from a linear-phase 2-D FIR filter, which serves as the initial filter.
 The structured controllability and observability Gramians $P^s$ and $Q^s$ serve as the foundation for this technique. 
 These Gramians are block diagonal positive-definite matrices that satisfy 2-D Lyapunov equations.
 An efficient method is used to compute these Gramians by minimizing the traces of $P^s$ and $Q^s$ under linear matrix inequalities (LMI) constraints.
 The use of these Gramians ensures that the resulting 2-D IIR filter preserves stability and can be implemented using a separable denominator 2-D filter with fewer coefficients than the original 2-D FIR filter. 
 Numerical examples show that the proposed method compares favorably with existing techniques.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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