<title>Nonlinear signal processing using index calculus DBNS arithmetic</title>
Bibliographic record
Abstract
This paper discusses the use of a recently introduced index calculus Double-Base Number System (IDBNS) for representing and processing numbers for non-linear digital signal processing; the target application is a digital hearing aid processor. The IDBNS representation uses 2 orthogonal bases (2 and 3) to represent real numbers with arbitrary precision. By restricting the number of digits to one or two, It is possible to efficiently represent the real number using the indices of the bases rather than the distribution of the digits. In this paper we discuss the use of the two-digit form of this representation (2-IDBNS) to efficiently perform arithmetic associated with the non-linear processing required to correct the usual forms of hearing loss in a digital hearing aid. The non-linear processing takes the form of dynamic range compression as a function of frequency band. Currently developed digital hearing instrument processors require large dynamic range representations (20 - 24 bits) in order to accurately generate the dynamic range compression associated with typical hearing loss. We show that the natural non-linear representation afforded by the IDBNS provides both a more efficient signal representation and a more efficient technique for processing the dynamic range compression. We pay particular attention to a novel technique of converting from a linear binary input directly to the 2-IDBNS representation using an observation of partial cyclic repetition in the indices along with near unity approximants.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.026 | 0.009 |
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".