A battery's electrochemical impedance response provides great insight about its internal electrochemical dynamics and state-of-health. This paper presents a method to efficiently obtain wide-bandwidth electrochemical impedance spectra using two-level (binary) perturbation sequences. In this study, a physically based battery model's current-voltage response is captured with state-space models using system-identification methods. However, any single identified model is accurate only within a specific, limited frequency range. A stitching procedure combines several state-space models to establish a composite state-space model that is accurate over a wide frequency range. A validation study shows excellent agreement between the impedance of the stitched state-space model and the original physically based battery model. The approach is equally applicable to extracting electrochemical impedance spectra from simulation models as for experimental investigations. (C) 2018 The Electrochemical Society.