A Minimum Variance Distortionless Response Spectral Estimator with Kronecker Product Filters
Bibliographic record
Abstract
Spectral estimation is of significant practical importance in a wide range of applications. This paper proposes a minimum variance distortionless response (MVDR) method for spectral estimation based on the Kronecker product. Taking advantage of the particular structure of the Fourier vector, we decompose it as a Kronecker product of two shorter vectors. Then, we design the spectral estimation filters under the same structure, i.e., as a Kronecker product of two filters. Consequently, the conventional MVDR spectrum problem is transformed to one of estimating two filters of much shorter lengths. Since it has much fewer parameters to estimate, the proposed method is able to achieve better performance than its conventional counterpart, particularly when the number of available signal samples is small. Also presented in this paper is the generalization to the estimation of the cross-spectrum and coherence function.
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How this classification was reachedexpand
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".