Acoustic spectral estimation using higher order statistics

Assuming an autoregressive (AR) filter model driven by a non-Gaussian white noise, we formulate a general parameter estimation problem. A maximum likelihood solution gives an AR estimate of the filter and the probability distribution function parameters for non-Gaussian input. The proposed method is optimal in the information theoretic sense, giving the most probable model for the source and filter under the higher order statistics constrains of the observed signal. Analysis of human singing voices and musical instruments is presented and its acoustic interpretation is discussed.