= Variance of a pedestal-corrected sample
The <variance of a pedestal-corrected sample> quantifies the random spread remaining after subtracting an estimated baseline from a signal acquisition. Subtracting a mean <reset charge-injection pedestal> removes an offset; it does not automatically remove <reset pedestal variance>. For a raw signal sample $Y$ and pedestal estimate $B$,
$$
\operatorname{Var}(Y-B)=\operatorname{Var}(Y)+\operatorname{Var}(B)-2\operatorname{Cov}(Y,B).
$$
The <covariance> term determines whether subtraction suppresses shared fluctuations or adds independent noise. The GUM's correlated-input rule gives this identity directly for the linear <measurement model> $f(Y,B)=Y-B$.<Guide to the expression of uncertainty in measurement by JCGM>[Section5.2.2, equation13]{ref}
Two correction procedures have different statistical consequences. First suppose signal acquisitions have independent pedestals $P_i$ of <variance> $\sigma_P^2$ and independent readout noise $\eta_i$ of <variance> $\sigma_\eta^2$. A separate mean of $M$ independent blank acquisitions, with individual <variance> $\sigma_B^2$, is reused for every signal sample:
$$
D_i=s+P_i+\eta_i-\overline B.
$$
After removing any constant means, independence gives
$$
\operatorname{Var}(D_i)=\sigma_P^2+\sigma_\eta^2+\frac{\sigma_B^2}{M},\qquad
\operatorname{Cov}(D_i,D_j)=\frac{\sigma_B^2}{M}\quad(i\ne j).
$$
Consequently, averaging $N$ corrected samples gives
$$
\operatorname{Var}(\overline D)=\frac{\sigma_P^2+\sigma_\eta^2}{N}+\frac{\sigma_B^2}{M}.
$$
The shared blank correction creates a common uncertainty floor, as in <shared calibration error>.
Alternatively, a baseline and signal reading from the same acquisition can share a fluctuating pedestal. In an idealized <correlated double sampling> model, $R=B_0+e_R$ and $Y=s+B_0+e_Y$, so $Y-R=s+e_Y-e_R$: the common $B_0$ cancels. Independent readout noises remain and their <variances> add. More generally, if paired readings each have <standard deviation>0.20millivolt and <correlation coefficient>0.9, their difference has <standard deviation>
$$
\sqrt{2(0.20)^2(1-0.9)}\,\mathrm{mV}\approx0.0894\,\mathrm{mV}.
$$
Treating that pair as independent would predict0.283millivolt instead.
An experimental assessment records paired zero-input samples at the actual acquisition delays and estimates their <covariance>, then distinguishes that procedure from reusing a separate blank mean. The ACF2101 datasheet specifies output noise and charge-transfer errors separately; a charge-transfer limit is not itself a pedestal <variance> or evidence for a particular correlation.<ACF2101 Low Noise, Dual Switched Integrator datasheet>[Printed p3, Output Noise and Charge Transfer Errors; p11, Charge Transfer]{ref}
Back to article page