Generalisation of linear prediction with autocorrelation method

A generalisation of conventional linear prediction (LP) is proposed. The method implements the prediction using a parallel structure, where the input is first filtered with two FIRs having zeros at z=1 and z=2. Two symmetric LP polynomials are then defined from the pre-filter outputs. The generalised LP inverse filter is obtained by convolving the symmetric polynomials with fixed pre-filters with zeros at z=±1 and then summing the obtained polynomials. It is shown that by selecting -12<1+1, the resulting all-pole filter is stable. Conventional LP is obtained by choosing 1=1. 0 and 2=-1.0.