設計多級多重取樣率FIR(Finiteimpulse response)樣本刪減/插值濾波器 時，Crochiere和Rabiner發展出以多級濾波器總長度或每秒乘法數為目標函數 之近似參數最佳化問題，傳統求解此參數最佳化問題為在預設的維度下以連續最佳化演算法先求出最佳參數，再在所有空間之最佳解中找出最接近因數分解形式整數解的間接方法。本文發展出直接因數分解的演算法可直接求得目標函數近似式之最佳整數解並以實際設計曲面說明，由此演算法所觀察到的性質可修正傳統設計曲線。

The main issue in designing a multistage decimator/interpolator system is to optimally decide the total lengths or the multiplications per second of the cascaded filters. Crochiere and Rabiner developed an approximated optimization problem based on these two objective functions. In early research， the number of stages and the optimal parameters could only be determined after a full investment of the minimum solutions， and then a heuristic procedure also needed to be employed to choose the integer factors. The proposed algorithm provides a direct factorization to find the true minimum solution of the constrained integer optimization problem. With this approach， the true integer solution of the constrained problem is obtained. A typical design surface is presented by the proposed approach. Based on the example， well-known design properties may be modified.