Inverse π-transformation in the linear speech prediction

A method is suggested for reconstruction of stable characteristic polynomial of a filter-predictor by its 'polynomial spectrum' (elementary stable polynomials of the first degree). The method is based on multiple repetition of inverse transformations forming the classic method of linear spectral pairs (frequencies) and additional transformations enabling to carry out the multiple repetitions of these transformations. The suggested inverse π-transformation is a reconstructing (orthogonal) transformation with respect to the direct π-transformation and makes it possible to apply the method of linear spectral frequencies of higher orders.