Estimation of transfer function parameters with output Fourier transform sensitivity vectors
Bibliographic record
Abstract
We derive a technique for estimating a small number of parameters of a spatially or temporally varying transfer function for which a parametric model is known. Such systems occur in transmission lines with faults or mismatches, ultrasonic imaging, semiconductor layering and tomography in various applications. We assume that it is important not only to know that a boundary exists but also to estimate the spatially parameters of the medium across the boundary. The method does not require that the input need be known, but it must be applied to the diverse paths simultaneously, such as with a plane wave hitting a plane surface. The output signals at the various points are time synchronous unless delay is the varying parameter. The transfer function model may be nonlinear in the parameters, and we may also have to estimate the nominal values around which the parameters are locally varying. The procedure is constructed in the context of estimating at any point in space the parameters of the system by using the eigenstructure of the covariance matrix of vectors whose elements are Fourier transform values of the responses. We require that the available responses in the spatial neighborhood are independent enough to yield a good estimate of the covariance matrix. As an example we examine the case of an unknown parameter in a thin layer between 2 semi-infinite layers.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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 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".