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This paper presents a time-domain method for electrochemical impedance spectroscopy (EIS) analysis using ordinary least squares (OLS). In this approach, an electrochemical device, e.g., fuel cell or battery, is perturbed galvanostatically by a small-signal sinusoid that is logarithmically swept in frequency. Using four-terminal sensing, voltage and current measurements are made over the course of the sweep and fit to swept sinusoid models using OLS. The interrelated amplitude, phase, and instantaneous frequency of the resulting waveforms are analyzed to reveal the device impedance as a function of frequency. The accuracy of the EIS technique was tested on a known resistive-capacitive circuit, and its performance was demonstrated using a single InDEC solid oxide fuel cell. Data from these tests are included and show good accuracy and high precision over the broad range of frequencies tested (100 mHz to 5 kHz).