Statistical noise characterization Repeating an experiment multiple times is the conceptually simplest way to determine its frequency dependent noise amplitude. However, the impedance of a battery depends sensitively on external parameters such as temperature, but also on potentially slowly relaxing kinetic effects in the active material or its surface if fast charge or discharge has been employed. Such factors may lead to fluctuations or drifts of the impedance that could easily surpass the intrinsic noise at a particular frequency. Consequences are twofold: the noise obtained when an experiment is repeated and analyzed independently at each frequency could be exaggerated, and causality of the impedance response could be violated. The latter effect may void the applicability of the DRT concept altogether, but at this point it is assumed that the system can be considered as quasi-stationary for each individual acquisition. The former effect leads to noise components at very low frequencies on the order of the repetition rate of the experiment. Under the assumption of independent and identically distributed (iid) Gaussian white noise for each data point, and the assumption of only a small noise variation between neighbouring frequencies in the EIS spectrum, the problem of very low frequency noise contributions and drifts can be mitigated by noticing that the noise variance of individual data points is a factor 2 smaller than the noise variance of the difference between two data points. The noise variance can then be estimated independently for the real and the imaginary part of the impedance using