Maximum likelihood spectral estimation and its application of narrowband speech coding

Using the maximum likelihood (ML) method the Itakura-Saito 1 spectral matching criterion is generalized to aperiodic and periodic processes having arbitrary model spectra. For the all-pole model, Kay's 2 covariance domain solution to the exact ML problem is cast into the spectral domain and used to obtain the exact solution for periodic processes. It is shown that if the number of independent power measurements greatly exceeds the model order, then the ML algorithm reduces to a pitch-directed, frequency domain version of Linear Predictive (LP) spectral analysis. Using a real-time vocoder based on the exact ML analysis revealed that, in contrast to standard LPC, the synthetic speech has the quality of being heavily smoothed. This suggests that it is generally incorrect to interpret LPC spectral matching in terms of the Itakura-Saito criterion.