Error propagation and numerical recovery for a class of parametric DSP algorithms

The error propagation in various useful order- and time-recursive DSP algorithms is studied. It is demonstrated that in all these algorithms there are two kinds of error due to finite precision: an erratic and a systematic one. Examples of both kinds of error are provided, and special emphasis is given to the study of the systematic truncation or round-off error. It is shown that in the Levinson-type and Schur-type algorithms for the solution of the FLP (forward linear prediction) and the FIR (finite impulse response) problem, there is one dominant source of systematic error, while in the l-step ahead case there are two sources of such error. Moreover, it is pointed out that in the fast Kalman algorithms there are two kinds of systematic error. Precise indicators of the exact magnitude of the finite precision error are given, and possible recovery techniques are proposed