Simulation of <b>1</b>/<i>f</i><sup><i>α</i></sup> noise for analytical measurements
Bibliographic record
Abstract
A simple procedure is described that can be used to generate 1/fα noise, also known as power law noise, in simulated analytical measurement vectors. Certain types of power law noise, such as pink noise (α=1), dominate many types of analytical signals, so its simulation is important in optimizing data processing strategies. In this work, simulated 1/fα error sequences are created directly from white noise via the theoretical measurement error covariance matrix (ECM) by rotation and scaling. The 1/fα ECM is obtained from the coefficients of a finite impulse response filter and is easily adapted to generate multiplicative 1/fα noise that is probably more common for analytical systems exhibiting proportional noise characteristics. Simulating 1/fα noise directly from the ECM offers two main advantages. First, 1/fα noise can be easily simulated in the presence of other common analytical measurement errors by additive combination of the ECMs. Second, the theoretical ECM can be used to model real experimental measurement noise. It is shown that the power spectral density function of measurement error sequences generated by the proposed method closely approximates the theoretical behaviour of 1/fα noise. To demonstrate the utility of this method in evaluating data processing methods, simulated data exhibiting 1/f (pink) noise is analyzed by maximum likelihood principal component analysis (MLPCA) that takes measurement error structure into account, and baseline noise is simulated using brown noise to test baseline fitting by asymmetric least squares (AsLS).
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".