最小最大最佳化頻譜近似FIR濾波器設計

Abstract

本篇論文在於找出一串有限長度正數列頻譜，使其能夠近似於一個已給定的非負頻譜。我們利用最小化最大誤差指標，及Parks-McClellan演算法，設計出具有最佳誤差的頻譜，並對此頻譜做限制式上的處理，來得到正數列頻譜，並將所得到之正數列頻譜利用分解理論做分解，並以FIR系統實現之。我們在此也舉出例子，來比較我們所設計出的頻譜其最大誤差，並討論其結果。最後我們利用不同權重函數K值的模擬而得出，在K值設定為2時正數列具有最佳之最大誤差。

The purpose of this thesis is searching for a finite-length positive sequence so that its spectrum can optimally approximate to a given spectrum. In this thesis, we use the Min-Max criterion and Parks-McClellan algorithm to design this optimal approximation error of spectrum. Moreover, we give constraint of this optimal spectrum to get the positive spectrum. Then the positive spectrum can be factored by Spectrum Factorization Theorem and can be realized by FIR system. Moreover, we also give some examples to compare with our spectrum with maximal approximation error and discuss its result. Finally, we simulate different weighting functions of K and give some comparisons. From the results we can get the optimal approximation error of positive spectrum when K equal to 2.