計畫名稱：可調式分數延遲FIR數位濾波器及可調式分數階FIR微積分器之新架構及其設計
執行起迄：2011/08/01~2012/09/30
總核定金額：528,000元
中文摘要：在本計畫中，我們提出一維及二維可調式分數延遲響應FIR數位濾波器之新架構及其設計。以二維濾波器而言，此新架構源自於其頻率響應之泰勒展開式，所衍生出前置濾波器與次濾波器前後串接之架構。前置濾波器為一一維微分器，而次濾波器則為一組二維象限對稱濾波器，此等均可以最小均方法設計。與傳統之方法比較，實驗數據顯示出，在性能較好之情況下，此新架構之濾波器其獨立係數之數目亦少許多；但缺點是系統之延遲時間較長。此二維濾波器之架構及設計亦可延伸至一維系統。 在本計畫中，我們亦提出可調式分數階之FIR數位微分器及積分器之新架構及其設計。以可調式分數階之FIR數位微分器而言，傳統架構中之次濾波器在本計畫中將由前置濾波器與改良式次濾波器前後串接之架構取代，如此較佳之性能及較低之成本均能兼顧。同樣地，此方法亦被使用於可調式分數階FIR數位積分器之設計。 因此，本計畫完成下列目標： ●二維可調式分數延遲響應FIR數位濾波器之新架構及其設計。 ●一維可調式分數延遲響應FIR數位濾波器之新架構及其設計。 ●寬頻帶可調式分數階之FIR數位微分器之新架構及其設計。 ●可調式分數階之FIR數位積分器之新架構及其設計。
英文摘要：In this project, a new structure is proposed for the design of variable fractional-delay (VFD) 2-D FIR digital filters. Based on the Taylor series expansion of the desired frequency response, a prefilter-subfilter cascaded structure can be derived. For the 1-D differentiating prefilters and the 2-D quadrantally symmetric subfilters, they can be designed simply by the least-squares method. Design examples show that the required number of independent coefficients of the proposed system is much less than that of the existing structure, while the performance of the designed VFD 2-D filters is still better under the cost of larger delays. Similarly, the proposed method can also applied for the design of VFD 1-D FIR digital filters. Moreover, a new structure is proposed for the design of wideband variable fractional-order (VFO) FIR differentiators in this project. Part of subfilters in the conventional structure are replaced by the cascade of a prefilter and the modified subfilters, such that the performance of the designed system can be improved as well as the computational cost can be reduced. Several examples will be presented to demonstrate the effectiveness of the proposed method. And the proposed structure and the design method are expected to be used for the design of VFO FIR integrators. Therefore, the objectives during the project’s year are listed as below: ●New structure and design for VFD 2-D FIR digital filters. ●New structure and design for VFD 1-D FIR digital filters. ●New structure and design for wideband VFO FIR differentiators. ●New structure and design for VFO FIR integrators.