On the Characterization and Measurement of Randomly Varying Filters

It is well known that time-invariant linear filters can be characterized by their impulse responses. In this paper, a method is presented for characterizing and measuring a class of randomly varying linear filters. The class of filters considered is constrained to have finite memory and bandwidth and is represented by a tapped delay fine with random tap multipliers having a stationary Gaussian multivariate distribution. The filter characterization allows the complete determination of the filter output statistics for any given deterministic input signal which is approximately time- and band-limited. These inputoutput relations are embodied in the filter mean and covariance transfer matrices. It is shown that these transfer matrices are observable in the sense that all of their coefficients are measurable, whereas the covariance matrix of the tap multipliers is not, in general, an observable. A measurement technique is described by which the transfer matrix coefficients can be determined.