Levinson-Type Ladder Algorithms

Abstract

In Sect. 6.8, we introduced the Burg algorithm as one possible method of solving the Normal Equations in the stationary case of linear prediction (2.48). Clearly, Burg’s technique is closely related to the explicit ladder algorithm of Table 6.1. Like the explicit ladder algorithm, Burg’s technique requires the explicit calculation of residual signal vectors. Such procedures are known to have poor numerical properties and a computational complexity that grows linearly with the data (record) length. On the other hand, the computation of ladder reflection coefficients requires knowledge only about the residual energies, rather than the residual signals themselves. This important fact gives rise to the central question, whether one can establish order recursions of residual energies, as a substitute for the cumbersome residual signal vector order recursions appearing in the explicit least-squares ladder algorithm (Table 6.1) and in the Burg type PARCOR ladder algorithm of Table 6.7.