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 methods of PTV digital filters described by transfer functions. However, few studies have been published on the design of high‐precision and high‐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, and stability of PTV state‐space digital filters. First, PTV state‐space digital filters are described and dual PTV state‐space digital filters and equivalent transformations of PTV state‐space digital filters are 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, asymptotic stability and bounded input‐bounded output stability of PTV state‐space digital filters are discussed. Finally, a numerical example is given to verify the foregoing analytic results.