Analytical finite precision results for Burg's algorithm and the autocorrelation method for linear prediction

This paper derives new analytical results for quantifying the performance degradation induced by finite precision arithmetic upon the autocorrelation method and Burg's algorithm for linear prediction. The main results are analytical derivations of the resulting error in the reflection coefficient computation due to finite precision (FP) arithmetic implementation. From analysis of the second-order system, it is shown that for the autocorrelation method, FP effects are more dominant for signals having spectral poles which are near the unit circle and the real axis in the z plane. In this circumstance, analytical results show that the autocorrelation method indeed has severe degradation due to FP implementation. However, analytical results show that Burg's algorithm has FP properties superior to the autocorrelation method. Finally, experimental results are presented which show very close agreement between the analytical derivations and experimental results.