Figure shows repeated EIS measurements of a button cell battery at a state of charge of 37.5%. The spectra exhibit variations beyond random noise, particularly at low frequencies. This suggest systematic influences on the experimental data that are not considered in the theoretical noise model . It shows that, due to drifts or very slow fluctuations, a direct use of a set of reference measurements is not sufficient for a selective characterization of frequency dependent random noise, which is necessary for the determination of weights for data fitting. Similar results have also been reported in a recent study with a carefully implemented and optimized experimental setup , which illustrates that the presented results are representative for EIS investigations of batteries. Considering difference values between neighbouring data points in the EIS spectrum, systematic contributions get reduced considerably and remain immediately apparent only in the low-frequency region of the real part of Z (Figure , bottom row). Using the difference method also along the dimension of the experiment repetition, as described by Equation , further reduces systematic contributions, facilitating a statistical analysis of random noise as required for a weighted DRT analysis. The noise standard deviation for the real and imaginary part of the data, calculated using Equation , is shown in Figure . The noise level is compared with a fit using the Agarwal model (Equation ). A good correspondence is observed over the whole frequency range for the imaginary part of the noise. The real part shows some deviations in the region below 0.1 Hz. As observed in the low frequency region of the real part of the impedance in Figure , there are some systematic drift or very low frequency residuals even when noise is estimated using the difference method. Apart from this, trends correspond well when comparing a statistical noise analysis and the Agarwal model. The values for α, β and γ are comparable when independently determined for the real and the imaginary part of the noise, hence the hypothesis in that σ r (ω) ≈ σ i (ω) is justified. Overall, this comparison shows that the noise estimated experimentally is consistent with what had been reported in literature for such experiments, hence the determined noise values are a suitable basis for the estimation of weights for a weighted DRT inversion.