The problem of quantization errors in digital filter design arises because of the practical necessity due to finite wordlength implementation. These errors are classified into coefficient quantization error and roung off error. In this paper, in order to analyze and reduce these errors, minimum ceefficient quantization realization is directly derived form impulse responese design specification. And using the equivalent transform relation between minimum coefficient quantization error and minimum roundoff error realizations, we synthesize an optimal realization state-space digital filter. This technique is analyzed by the simulation of an approximated 3rd model, which shows that it is superior to direct or cascade state-space digital filter in quantization errors.