Computer simulation studies of a simplified model for a certain class of autoregressive systems

An autoregressive (AR) systemx{n} = \Sigma\min{i=1}\max{M} a_{i}(n) x(n-i) + A(n) w(n)where{a_{i}(n)}, and A(n) are general stationary stochastic processes and w(n) is white noise, is well modeled by a similar equation in which the random processes are replaced by their averages, if the resulting constant coefficient model is sufficiently lowpass, low gain (LPLG) [1]. By computer simulation, we investigate the performance of this approximation for various AR systems. It is found that "sufficiently LPLG" implies a very restricted class (very LPLG) for the general case of unknown (large) perturbations on{a_{i}(n), A(n)}. Only as the perturbations become small can the very LPLG restriction be relaxed.