FUNDAMENTAL-STUDY OF PERIODICALLY TIME-VARYING STATE-SPACE DIGITAL FILTERS-STATISTICAL ANALYSIS, SCALING, AND STABILITY

Analyses of periodically time-varying (PTV) digital filters that have been published deal with the fundamental properties and the design met hods of PTV digital filters described by transfer functions. However, few studies have been published on the design of high-precision and hi gh-efficiency PTV digital filters with minimum roundoff noise, minimum coefficient sensitivity, and model reduction. To analyze these design problems, this paper reports on the statistical analysis, scaling, an d stability of PTV state-space digital filters. First, PTV state-space digital filters are described and dual PTV state-space digital filter s and equivalent transformations of PTV state-space digital filters ar e defined. Then covariance of the states and variance of the output in response to a white Gaussian noise input are analyzed statistically. Based on these results, a scaling analysis is presented. Also, asympto tic stability and bounded input-bounded output stability of PTV state- space digital filters are discussed. Finally, a numerical example is g iven to verify the foregoing analytic results.