102學年度：廣域可調分數延遲FIR數位濾波器之設計及其在可調梳型濾波器系統之應用
計畫名稱：廣域可調分數延遲FIR數位濾波器之設計及其在可調梳型濾波器系統之應用
執行起迄：2013/08/01~2014/08/31
總核定金額：653,000元
中文摘要：在本計畫中，我們將致力於廣域可調分數延遲FIR數位濾波器之設計及其應用之研究。傳統上，可調分數延遲數位濾波器其延遲可調範圍均限定在一個單位以內，過去一、二十年已有諸多文獻深入探討其架構與設計，而其在通訊系統與訊號處理之應用已為眾所周知。然而，可在較大範圍可調之延遲FIR數位濾波器，尚無文獻探討其架構與設計。 當分數延遲FIR數位濾波器於大範圍延遲變化時，從其濾波器係數變化之軌跡中可發現傳統以多項式取代法為基點所提出之法羅架構(Farrow structure)已無法滿足廣域可調分數延遲FIR數位濾波器之需求。因此在本計畫中我們將可實現sinc函數轉換之電路與上述之法羅架構串接，以實現廣域可調分數延遲FIR數位濾波器之架構。至於其濾波器係數可以一般最小均方法求之。 廣域可調分數延遲FIR數位濾波器最典型之應用當屬可調梳型濾波器系統之實現。由於可調梳型濾波器系統其相關延遲係數變化之範圍甚大，本計畫之標的正足以滿足之，亦可降低整體系統之複雜度。 當然本計畫所提出之廣域可調分數延遲FIR數位濾波器亦可充當一般可調分數延遲數位濾波器，整體系統之複雜度亦可大幅下降。 由於廣域可調分數延遲FIR數位濾波器之架構與設計為首次提出，相信其當有許多潛在之應用。 本計畫完成之目標如下： A. 提出廣域可調分數延遲FIR數位濾波器之架構與設計。 B. 廣域可調分數延遲FIR數位濾波器在梳型濾波器系統之應用。 C. 以廣域可調分數延遲FIR數位濾波器之架構實現一般可調分數延遲數位濾波器，並完成其設計。
英文摘要：In this project, the structure and design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters will be proposed. With respect to the conventional VFD filters which are designed such that their delays are adjustable within one unit, the proposed VFD FIR filters are designed such that their delays can be tuned within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this project, least-squares method will be adopted to design WR-VFD FIR filter. However, when it is applied to construct a variable comb filter which is an IIR system, stability constraint must be considered, and the technique of quadratic programming and a strategy of sampling points for stability constraint are proposed to design a stable variable comb filter. The proposed method can also be applied to design a general VFD FIR filter, and it is found that the number of subfilters of VFD filters can be reduced drastically. The objectives have been achieved during the project’s year are listed as below: 1. Design of wide-range variable fractional-delay (WR-VFD) FIR digital filters. 2. Application of WR-VFD FIR filters in comb filter systems. 3. Application for the design of general VFD FIR digital filters.
執行起迄：2013/08/01~2014/08/31
總核定金額：653,000元
中文摘要：在本計畫中，我們將致力於廣域可調分數延遲FIR數位濾波器之設計及其應用之研究。傳統上，可調分數延遲數位濾波器其延遲可調範圍均限定在一個單位以內，過去一、二十年已有諸多文獻深入探討其架構與設計，而其在通訊系統與訊號處理之應用已為眾所周知。然而，可在較大範圍可調之延遲FIR數位濾波器，尚無文獻探討其架構與設計。 當分數延遲FIR數位濾波器於大範圍延遲變化時，從其濾波器係數變化之軌跡中可發現傳統以多項式取代法為基點所提出之法羅架構(Farrow structure)已無法滿足廣域可調分數延遲FIR數位濾波器之需求。因此在本計畫中我們將可實現sinc函數轉換之電路與上述之法羅架構串接，以實現廣域可調分數延遲FIR數位濾波器之架構。至於其濾波器係數可以一般最小均方法求之。 廣域可調分數延遲FIR數位濾波器最典型之應用當屬可調梳型濾波器系統之實現。由於可調梳型濾波器系統其相關延遲係數變化之範圍甚大，本計畫之標的正足以滿足之，亦可降低整體系統之複雜度。 當然本計畫所提出之廣域可調分數延遲FIR數位濾波器亦可充當一般可調分數延遲數位濾波器，整體系統之複雜度亦可大幅下降。 由於廣域可調分數延遲FIR數位濾波器之架構與設計為首次提出，相信其當有許多潛在之應用。 本計畫完成之目標如下： A. 提出廣域可調分數延遲FIR數位濾波器之架構與設計。 B. 廣域可調分數延遲FIR數位濾波器在梳型濾波器系統之應用。 C. 以廣域可調分數延遲FIR數位濾波器之架構實現一般可調分數延遲數位濾波器，並完成其設計。
英文摘要：In this project, the structure and design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters will be proposed. With respect to the conventional VFD filters which are designed such that their delays are adjustable within one unit, the proposed VFD FIR filters are designed such that their delays can be tuned within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this project, least-squares method will be adopted to design WR-VFD FIR filter. However, when it is applied to construct a variable comb filter which is an IIR system, stability constraint must be considered, and the technique of quadratic programming and a strategy of sampling points for stability constraint are proposed to design a stable variable comb filter. The proposed method can also be applied to design a general VFD FIR filter, and it is found that the number of subfilters of VFD filters can be reduced drastically. The objectives have been achieved during the project’s year are listed as below: 1. Design of wide-range variable fractional-delay (WR-VFD) FIR digital filters. 2. Application of WR-VFD FIR filters in comb filter systems. 3. Application for the design of general VFD FIR digital filters.
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