在此篇論文中，我們討論過濾器設計的問題，在容許的最大誤差限制下，用半無限二次規劃方法逼近最佳解，並探討誤差分析。在論文中，把原問題準換成二次半無限規劃問題，使用我們的演算法，並且給出我們演算法的收斂性證明。最後，我們使用我們的演算法解決實務上的幾個例子並加以分析。

This paper is concerned with the design of linear-phase finite impulse response (FIR) digital filters which the weighted least square error is minimized, subject to maximum error constraints. The design problem is formulated as a quadratic semi-infinite optimization problem.
We solve this problem by using relaxed cutting-plane scheme.
The connection between the primal and the dual problems are established. When a cutting-plane method is applied to solve a quadratic semi-infinite programming problem, basically, it solves a sequence of finite-dimensional quadratic programs and shows that the corresponding solution sequence converges to the optimal solution of the original problem. Hence, the optimal solution to the original problem can be readily obtained and the convergence proof of our algorithm is given.
Finally, examples are solved using the proposed computational procedure.

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