Optimum time–frequency distribution for detecting a discrete-time chirp signal in noise
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Bibliographic record
Abstract
In the continuous-time domain, maximum-likelihood (ML) detection of a chirp signal in white Gaussian noise can be done by maximising (with respect to signal parameter arguments) the line-integral transform (LIT) of the classical Wigner distribution (of the observed signal). The LIT is known variously as the Hough transform and the Radon transform. For discrete-time signals, the Wigner-type distribution defined by Claasen and Mecklenbrauker has become popular as a signal analysis tool. Moreover, it is commonly believed that ML detection of a discrete-time chirp signal in independent and identically distributed (i.i.d.) Gaussian noise can be done by maximising the LIT of the Wigner–Claasen–Mecklenbrauker distribution (WCMD). This belief is false and results in loss of performance. The authors derive a Wigner-type distribution for discrete-time signals such that ML detection of a discrete-time chirp signal in i.i.d. Gaussian noise can be done by maximising the LIT of this distribution. Simulated receiver operating curves showing the performance advantage of the new method over the WCMD-based method are provided. The signal parameter values that maximise the LIT are taken as estimates of the actual parameters. The authors provide simulation results showing that the parameter estimates obtained using the new method are more accurate than those obtained using the WCMD-based method. For the WCMD-based method, the range of unambiguously measurable frequencies (RUMF) is [−π/2, π/2]. For the new method, the RUMF is [−π, π].
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 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