最小平方正數列頻譜近似FIR濾波器設計

Abstract

本篇論文的主題在找出一串有限長度的正數列，使其頻譜能夠近似於一個巳給定的非負頻譜。此問題可表示為凸性半無限維最佳化問題(convex semi-infinite optimization problem)。我們使用最小平方誤差指標及Lagrange multiplier為基礎發展一套適用於本系統的演算法，其優點可以將原來半無限維(semi-infinite)最佳化問題轉換成有限維度(finite-dimensional)最佳化問題來解決。文中將會用三種演算法來做比較，並以幾個不同階數的例子來探討此三個演算法的優缺點。

The purpose of this thesis is searching for a finite-length positive sequence so that its spectrum can optimally approximate to a given spectrum. The design problem is formulated as a convex semi-infinite optimization problem. The algorithm uses the least square criterion and Lagrange multipliers on each iteration. The advantage of this approach is that the original semi-infinite programming problem can be solved directly as a finite-dimensional optimization problem. In this thesis we will use three algorithms and discuss their advantages and disadvantages by using some numerical examples.