In this thesis, a novel approach of synthesizing the finite-precision digital fil-tering scheme for noise cancellation of wearable devices such as ECG recorders is presented. By using the proposed method and Schur Decomposition Algorithm, one may transfer any original given filter realization to a sparse normal-form structure. It is shown that sparse normal-form realizations are with minimal finite word-length (FWL) sensitivity, limit-cycle-free property, and highly computational efficiency. Moreover, we propose an improved algorithm can auto scale the matrix gain between the input and output matrices of a state-space IIR digital filter reali-zation. This may highly reduce the probability of overflow and underflow effects. Finally, a numerical example is proposed to verify our proposed approach.