TET Signal & Linearization Lab

TET signal & logarithmic linearization

The synthetic data below is generated from the full series solution — the same one given in the article, summed over 40 odd-numbered eigenmodes. The reduction then fits only the first-term approximation, exactly as a real analysis does. The gap between them is the recovered-value error: model-form mismatch, plus measurement noise, plus error in estimating the two endpoints. Watching it shrink as early points are excluded is the entire argument for the 0.1–0.8 window.

Full-series synthetic record V₁ estimated from the data Points inside the fit window Transformed points excluded by the window First-term linear regression

Preset:

True α

Length L

Voltage noise

Fit start T*

Window:

Generate with: first load uses a fixed seed

Model: one-dimensional transient conduction in a suspended specimen with both ends held isothermal. Generation uses T* = (96/π⁴)Σ(1−exp[−(2m−1)²π²Fo])/(2m−1)⁴; the late-time first eigenmode gives 1−T* ≈ (96/π⁴)exp(−π²αt/L²), so reduction fits ln|V−V₁| = −π²αt/L² + D with the modal amplitude 96/π⁴ absorbed into D. V₀ comes from a pre-trigger baseline and V₁ from the late plateau — both estimated, not assumed. Radiation, convection, coating and contact effects are excluded. This simplified model illustrates fitting behavior only — the regression standard error it reports is not a measurement uncertainty.