Abstract
本篇論文提出一種新的用反覆加權最小平方近似法設計無限脈衝響應數位濾波器。祁教授忠勇及邱學長徐禮提出一個加權最小平方近似法來設計有限脈衝響應數位濾波器，我們將此加權最小平方近似法做適當的修改用以設計無限脈衝響應的數位濾波器。當所希望的頻率響應( 即振幅響應及相位響應 )均己知時，所設計出來的無限脈衝響應數位濾波器，其誤差的絕對值是近似等漣波的，但它並不保証是穩定，若所希望的相位響應是線性相位時，適當地增加群延遲於所希望的群延遲響應，則所設計出來的濾波器會是穩定的濾波器。若我們加一些限制於濾波器的係數時，本論文所提出來的近似法也可用以設計全通濾波器，而所設計出來的全通濾波器之相位誤差也是等漣波的，同樣地它並不保証是穩定的，而適當地增加群延遲於所希望的群延遲響應，則所設計出的濾波器將是穩定的濾波器。在另一方面，當只有振幅響應是已知時，我們所設計出來的濾波器是一最小相位的濾波器。This thesis proposes a new approximation method using theweighted least squares (WLS) algorithm for the design of IIRfilters. The WLS algorithm used by Chi and Chiou's approxima-tion method for the design of FIR filters is modified for thedesigned of IIR filters. When the desired frequency responseincluding magnitude and phase is specified, the designed IIRfilter is nearly equiripple in absolute (complex) approxima-tion error, but it is not guaranteed to be stable. The pro-posed approximation method can also be used for the design ofallpass filters by taking into account of some constraint infilter coefficients. The designed allpass filter is equiripplein phase and will be stable by adding an appropriate positivegroup delay to the desired group delay response. On the otherhand, when only magnitude of the desired frequency response isspecified, the designed IIR filter is minimum-phase. Six de-signed examples are provided to support the proposed approxi-mation method. Finally, we draw some conclusions.