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This paper introduces the stochastic Gabor function (SGF), an excitation waveform that can be used to design optimal excitation pulses for Electrical Impedance Spectroscopy (EIS) of the brain. The SGF is a Gaussian function modulated by uniformly distributed noise; it has wide frequency spectrum representation regardless of the stimuli pulse length. The SGF was studied in the time-frequency domain. As shown by frequency concentration measurements, the SGF is least compact in the sample frequency phase plane. Numerical results obtained by using a realistic human head model indicate that the SGF may allow for both shallow and deeper tissue penetration than is currently obtainable with conventional stimulus paradigms, potentially facilitating tissue subtraction assessment of parenchymal dielectric changes in frequency. This could be of value in advancing EIS of stroke and hemorrhage.