Efficient generation of long-memory signals using lattice structures

Abstract

Two new algorithms are presented for the generation of long-memory signals using lattice filter structures. Currently, the best known generation methods make use of the Levinson-Durbin recursion which requires O(N/sup 2/) computations to compute the model. Two new synthesis methods for fractional difference signals are given which exploit the a priori knowledge of the partial correlation coefficients to reduce the computations by an order of magnitude from O(N/sup 2/) to O(N). A synthesis technique is also given for fractional noise signals using lattice filters where the lattice coefficients are determined using the Schur algorithm, again with a computational savings over the Levinson-Durbin recursion. The lattice filter also has the distinct advantage of guaranteeing a stable system which is an important issue for long-memory signals which have a fractional order pole on the unit circle.