Normalized Ladder Form of the Residual Energy Ratio Algorithm for Autoregressive Estimation via Projections

摘要

A square-root normalized ladder algorithm is given for the residual energy ratio (RER) method of autoregressive estimation. Dirac's bra-ket notation for elements of a Hilbert space is used in an approach similar to that of Lee and Morf, but an additional related Hilbert space and its corresponding projection operators are required. A stable synthesis filter is guaranteed by the resulting partial correlation estimates. A way of casting the algorithm in a form suitable for implementation by a CORDIC processor is revealed. The normalized covariance form is shown to correspond to an RER formulation where the prediction error energies are properly chosen.