On spectral theory of cyclostationary signals in multirate systems
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Bibliographic record
Abstract
This paper studies two problems in the spectral theory of discrete-time cyclostationary signals: the cyclospectrum representation and the cyclospectrum transformation by linear multirate systems. Four types of cyclospectra are presented, and their interrelationships are explored. In the literature, the problem of cyclospectrum transformation by linear systems was investigated only for some specific configurations and was usually developed with inordinate complexities due to lack of a systematic approach. A general multirate system that encompasses most common systems-linear time-invariant systems and linear periodically time-varying systems-is proposed as the unifying framework; more importantly, it also includes many configurations that have not been investigated before, e.g., fractional sample-rate changers with cyclostationary inputs. The blocking technique provides a systematic solution as it associates a multirate system with an equivalent linear time-invariant system and cyclostationary signals with stationary signals; thus, the original problem is elegantly converted into a relatively simple one, which is solved in the form of matrix multiplication.
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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 | 0.001 | 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 | 0.001 |
| 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