Time-Frequency Analysis via Ramanujan Sums
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Bibliographic record
Abstract
Research in signal processing shows that a variety of transforms have been introduced to map the data from the original space into the feature space, in order to efficiently analyze a signal. These techniques differ in their basis functions, that is used for projecting the signal into a higher dimensional space. One of the widely used schemes for quasi-stationary and non-stationary signals is the time-frequency (TF) transforms, characterized by specific kernel functions. This work introduces a novel class of Ramanujan Fourier Transform (RFT) based TF transform functions, constituted by Ramanujan sums (RS) basis. The proposed special class of transforms offer high immunity to noise interference, since the computation is carried out only on co-resonant components, during analysis of signals. Further, we also provide a 2-D formulation of the RFT function. Experimental validation using synthetic examples, indicates that this technique shows potential for obtaining relatively sparse TF-equivalent representation and can be optimized for characterization of certain real-life signals.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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