頻譜近似之FIR濾波器設計

Abstract

本論文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頻譜。如此，新的有限長度正數列之頻譜即可作適當的分解，並以FIR系統作近似。文中以有效集法為基礎發展一套適用於本系統的演算法，其特點在於一次處理多個限制條件，以提昇演算效率，並以幾個階數不同的例子來驗證此法之可行性。將分解理論應用於新的有限長度正數列之頻譜的結果，證明此方法確實可找出一具有最小相位特性的FIR系統來作頻譜近似。

The subject of this thesis is to find a finite-length positive sequence that its spectrum is approximate to a given spectrum in the least-mean-square sense. Thus, the new spectrum can be properly factorized and be approximated by an FIR system. The algorithm is based on the active set method and its characteristic is to deal with several constraints at the same iteration to improve the efficiency. We test and verify this algorithm by some numerical examples with different orders. After applying the factorization theorem on the new spectrum, we can certainly find a minimum-phase FIR system for spectrum approximation.