Recursive RC Modeling for Time-Domain Estimation of the Distribution of Relaxation Times

We propose a time-domain method for estimating the Distribution of Relaxation Times (DRT) in electrochemical systems based on a recursive RC modeling framework. By discretizing the system response via bilinear transformation, this approach enables direct reconstruction of the DRT from arbitrary current excitation signals, without relying on frequency-domain impedance data or predefined excitation profiles, as required by established methods such as pulse-fitting. The method integrates multiple electrochemical contributions into a unified linear model and solves the resulting inverse problem using nonnegative least squares with Tikhonov regularization. Validation with synthetic and experimental data demonstrates high accuracy, numerical stability, and excellent agreement with conventional impedance spectroscopy. The approach significantly reduces measurement time, especially in the low-frequency regime, and offers robust performance under realistic noise conditions.