COEFFICIENT SENSITIVITY ANALYSIS OF PERIODICALLY TIME-VARYING STATE-SPACE DIGITAL-FILTERS

This paper considers an analysis of statistical coefficient sensitivit y and frequency coefficient sensitivity of Periodically Time-Varying ( PTV) state-space digital filters. A statistical coefficient sensitivit y is defined by using a virtual PTV state-space digital filter in whic h the periodically time-varying coefficients are stochastically varyin g. In order to analyze frequency coefficient sensitivity, a transfer f unction, which is called Output Sampling Polyphase (OSP) transfer func tion, is defined and expressed in terms of the coefficients of PTV sta te-space digital filters in a closed form. A frequency coefficient sen sitivity is defined as an integral measure of the OSP transfer functio n with respect to the coefficients. It turns out that although the def initions of the two kinds of coefficient sensitivities are extremely d ifferent, their expressions are the same and closely related to the co ntrollability and observability Grammians of PTV state-space digital f ilters. Also, some considerations for the minimization of the coeffici ent sensitivity are discussed. Finally, a numerical example is given t o verify the analysis above and to show the dependence of the coeffici ent sensitivity on structure of PTV state-space digital filters.