近似最佳化正數列頻譜FIR濾波器設計

Abstract

本研究的主題在找出一串有限長度的正數列，使其頻譜在最小平方差的指標下，能夠最佳近似一個已給定的正或非正的頻譜。此有限長度正數列所產生的頻譜便可利用頻譜分解理論做分解，並用FIR系統做實現。將頻譜分解理論應用於求得的有限長度正數列之頻譜的結果，確實可找出一具有最小相位特性的FIR系統來做頻譜近似。文中將會用三個演算法來做比較，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 research is searching for a finite-length positive sequence so that its spectrum can optimally approximate to a given spectrum in the least-mean-square. This spectrum which is generated by this finite-length positive sequence can be factored by Spectrum Factorization Theorem and be realized by FIR systems. The result that apply Spectrum Factorization Theorem to spectrum of the new finite-length positive sequence can show that this theorem certainly find a minimum-phase FIR system for approximating the spectrum. In this report we will use three algorithms and discuss their advantages and disadvantages by using some numerical examples.