Piecewise continuous linear interpolation of the sine function for Direct Digital Frequency Synthesis
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Bibliographic record
Abstract
This paper discusses the design of Direct Digital Frequency Synthesizers (DDFS) based on the linear interpolation of the sine function. The problem of approximating the sine function within a desired error bound is specifically considered. The use of linear segments is favorable for hardware implementation because of the low processing complexity requirements. A relation between the minimum number of linear segments, the resolution with which segment slopes are expressed, and the achievable precision is derived. Tradeoffs between memory storage requirements and computational complexity are identified, and architectural and implementation issues are discussed. Example designs achieving 8, 10 and 12 bits of amplitude resolution with 59, 77 and 86 dBc of Spurious Free Dynamic Range (SFDR) are presented.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it