In this paper, the output error variance due to the differential vcariation of the state-space coefficient [ABCD], which is the coefficient quentization error, is normalized on the variance for cases that infinite wordlength state-space digital filter is realized by the finite one. That is, defining S as the statistical sensitivity and extending controllability gramian, observability gramian, and 2nd order mode analysis method to the state space digital filter, we synthesize the realization structure with the minimum statistical sensitivity and prove the effecency of the minimum statistical sensitivity structure synthesis by the simulation.