基於總合性最小平方誤差準則之複係數特徴濾波器設計

Abstract

特徵濾波器最初是基於最小平方誤差準則來設計想要的頻率響應，後來發展出實係數特徵濾波器基於總合性最小平方誤差準則，將原本的最小平方誤差準則用總合性最小平方誤差準則來取代，兩者相比較之下，總合性最小平方誤差準則不但保有原本的特性，並且改善了演算過程中需選擇參考頻率的缺點，進而更降低其演算的複雜度。 本文主要是將特徵濾波器基於總合性最小平方誤差準則的觀念加以延伸，原本只應用在實係數領域進而擴展到複係數領域，而這樣的擴展讓基於總合性最小平方誤差準則的特徵濾波器在應用面得以完備，並且改善了相位響應的近似。

At first, the eigenfilter is designed based on the least squares error criterion to obtain the desired frequency response. Then the criterion is later extended to total least squares error. By comparison with least squares error criterion, the eigenfilter designed based on total least squares criterion retains not only the original properties but also bypasses the reference frequency selection to simplify the algorithm. The contribution of this paper is to extend the real coefficient eigenfilter to the complex coefficient eigenfilter based on the concept of total least squares error criterion. This extension completes the application of the eigenfilter and improve the approximation of phase response.