A pole-zero model for cepstrally smoothed speech spectra

In this paper a new method for representation of cepstrally smoothed speech spectra by a pole-zero model is presented. In this method the cepstrally smoothed log spectrum is split into two parts, one corresponding to the response of the numerator polynomial of the model transfer function and the other part to the response of the denominator polynomial of the model transfer function. The decomposition is achieved by using the properties of the derivative of phase spectra of minimum phase signals. The inverse of each of these responses is approximated by a small number of auto-regressive coefficients. The method is illustrated with several examples of speech spectra. The residual from the inverse pole-zero model system can be used to obtain information about the excitation signal. The technique proposed in this paper can be used to represent any arbitrary smoothed log spectrum by a pole-zero model of appropriate order.