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Neuronal systems receive inputs from other structures, transform these signals, and then pass the processed signals onto other brain areas. The nature of these transformations and their roles in information processing are poorly understood. Motivated by experiments demonstrating that the olfactory bulb separates odor representations, we seek a minimal biological model of a neuronal system that can separate a mixture of incoming signals. As a first step, we consider inputs that are the superposition of two periodic spike trains. We ask what network properties would allow the system to separate the two frequencies; that is, some of the output cells should fire at one of the incoming frequencies and other output cells should fire at the second frequency. We present and analyze a simple neuronal network that is remarkably successful at separating frequencies. Our analysis uses methods from discrete dynamics and the geometric theory of singular perturbations.