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In this paper, we apply a new time-frequency spectral estimation method for multichannel data to epileptiform electroencephalography (EEG). The method is based on the smooth localized complex exponentials (SLEX) functions which are time-frequency localized versions of the Fourier functions and, hence, are ideal for analyzing nonstationary signals whose spectral properties evolve over time. The SLEX functions are simultaneously orthogonal and localized in time and frequency because they are obtained by applying a projection operator rather than a window or taper. In this paper, we present the Auto-SLEX method which is a statistical method that 1) computes the periodogram using the SLEX transform, 2) automatically segments the signal into approximately stationary segments using an objective criterion that is based on log energy, and 3) automatically selects the optimal bandwidth of the spectral smoothing window. The method is applied to the intracranial EEG from a patient with temporal lobe epilepsy. This analysis reveals a reduction in average duration of stationarity in preseizure epochs of data compared to baseline. These changes begin up to hours prior to electrical seizure onset in this patient.