In this thesis, we will investigate how to establish the computer program for implementing infinite impulse response (IIR) digital filters with L2-scaling constraints under fixed-point considerations. The L2 sensitivity function will be used as the cost function during the op-timization procedure. In specific, The developed program will lead to a synthesized filter structure with minimal L2 sensitivity subject to L2-scaling constraints. In this thesis, several digital filter structures are provided for illustrating the effectiveness of the proposed approach.