Coefficient sensitivity analysis of periodically time-varying state-space digital filters

This paper considers an analysis of statistical coefficient sensitivity and frequency coefficient sensitivity of Periodically Time-Varying (PTV) state-space digital filters. A statistical coefficient sensitivity is defined by using a virtual PTV state-space digital filter in which the periodically time-varying coefficients are stochastically varying. In order to analyze frequency coefficient sensitivity, a transfer function, which is called Output Sampling Polyphase (OSP) transfer function, is defined and expressed in terms of the coefficients of PTV state-space digital filters in a closed form. A frequency coefficient sensitivity is defined as an integral measure of the OSP transfer function with respect to the coefficients. It turns out that although the definitions of the two kinds of coefficient sensitivities are extremely different, their expressions are the same and closely related to the controllability and observability Grammians of PTV state-space digital filters. Also, some considerations for the minimization of the coefficient sensitivity are discussed. Finally, a numerical example is given to verify the analysis above and to show the dependence of the coefficient sensitivity on structure of PTV state-space digital filters