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This paper describes an analytic technique, whereby the transfer function of a pole-zero model of the speech production process may be derived from the speech signal. The process involves fitting the model to the smoothed short-time amplitude spectrum which is derived by processing the speech signal through a bank of fourth-order, bandpass filters and cepstrally smoothing the output. The order of the pole-zero model is defined by twice the number of spectral maxima in the derived spectrum. The fitting criteria are specified on a perceptual basis rather than the usual least-squared error, the model being constrained to fit exactly the maxima and minima of the spectral curve.