Finite precision arithmetic and the Schur algorithm

The numerical behavior of the Schur algorithm under fixed-point arithmetic conditions is investigated. It was found that the variance of the reflection coefficient estimates is large when the autocorrelation coefficients used to obtain the estimates are obtained from a narrowband low-pass signal. This is because such signals yield ill-conditioned autocorrelation matrices and is not due to numerical instability in the Schur algorithm. The effects of quantization errors tend to propagate through the later stages of the reflection coefficient computation in this instance. As a result, the Schur algorithm has numerical properties similar to those of the Durbin algorithm