Insights Into Frequency-Invariant Beamforming With Concentric Circular Microphone Arrays
Bibliographic record
Abstract
This paper studies the problem of frequency-invariant beamforming with concentric circular microphone arrays (CCMAs) and presents an approach to the design of frequency-invariant and symmetric beampatterns. We first apply the Jacobi-Anger expansion to each ring of the CCMA to approximate the beampattern. The beamformer is then designed by using all the expansions from different rings. In comparison with the existing work in the literature where a Jacobi-Anger expansion of the same order is applied to different rings, here in this contribution the order of the Jacobi-Anger expansion at a ring is related to its number of sensors and, as a result, the expansion order at different rings may be different. The developed approach is rather general. It is not only able to mitigate the deep nulls problem in the directivity factor and the white noise gain, that is common to circular microphone arrays (CMAs), and improve the steering flexibility, but is also flexible to use in practice where a smaller ring can have less microphones than a larger one. We discuss the conditions for the design ofNth-order symmetric beampatterns and examples of frequency-invariant beampatterns with commonly used array geometries such as CMAs, CMAs with a sensor at the center, and CCMAs. We show the advantage of adding one microphone at the center of either a CMA or a CCMA, i.e., circumventing the deep nulls problem caused by the 0th-order Bessel function.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".