TY - JOUR

T1 - Coefficient Sensitivity Analysis of Periodically Time-Varying State-Space Digital Filters

AU - Yang, Xuedong

AU - Kawamata, Masayuki

AU - Higuchi, Tatsuo

PY - 1994/1/1

Y1 - 1994/1/1

N2 - 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.

AB - 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.

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U2 - 10.1109/82.318941

DO - 10.1109/82.318941

M3 - Article

AN - SCOPUS:0028480146

VL - 41

SP - 526

EP - 536

JO - IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

JF - IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

SN - 1057-7130

IS - 8

ER -