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This paper introduces a brain-like neural model for sound processing. The periodicity analyzing network (PAN) is a bio-inspired neural network of spiking neurons. The PAN consists of complex models of neurons, which can be used for understanding the dynamics of individual neurons and neuronal networks. On a technical level, the PAN is able to compute the ratio of modulation and carrier frequency of harmonic sound signals. The PAN model may, therefore, be used in audio signal processing applications, such as sound source separation, periodicity analysis, and the cocktail party problem.