The same noisy transients (fixed random seed) are reduced two ways over the same shared fit window [Fostart, Foend], from the same original acquisition and noise realization: a full-series unweighted least-squares fit, and ordinary linear regression on ln|1−T*| over the same eligible points — any point with 1−T* ≤ 0 is counted and excluded, because its logarithm is undefined. Drag the window and watch what actually governs the linearized route: the transform is remarkably straight from very early Fo — the higher modes die fast, which is why the fit start is the stable choice — but pushing the window’s end toward the noise floor amplifies noise heteroscedastically and eventually makes the logarithm undefined, and a short late window has little slope leverage. Same data, same window, two honest answers with different failure modes.
Model: series-solution data plus Gaussian noise on T*. Both routes use the same acquisition, noise realization and nominal time window; no point is included or excluded based on its own noisy value. The full-series route retains all points in that window; the logarithmic route uses the subset for which 1−T* > 0 — a logarithm does not exist otherwise — with excluded points reported explicitly rather than silently absorbed. The plotted scatter, both fitted lines and the single-shot slope standard error all come from one designated display realization; the Monte-Carlo mean ± SD lines summarize 25 realizations separately. A standard error describes scatter around an estimate — it does not by itself reveal systematic bias, which is why the tool reports mean bias alongside it. Weighted least squares or maximum-likelihood estimators on the raw-voltage noise model can outperform both simple routes; this tool compares the two simplest on equal terms. Schematic teaching tool, not an instrument.