計畫名稱：以經馴服的二次式規畫法設計可調分數延遲IIR數位濾波器
執行起迄：2014/08/01~2015/10/31
總核定金額：529,000元
中文摘要：近年來，可調式分數延遲響應數位濾波器被廣泛應用於訊號處理及通訊系統。自法羅架構(Farrow structure)於1988年被提出後，FIR型式、IIR型式及全通(allpass)型式分別被用來實現該類濾波器。相較於FIR型式及全通型式之架構，IIR型式之可調式分數延遲響應數位濾波器因整體平均延遲時間較小，而自成一族群。因可調式分數延遲響應IIR數位濾波器之係數數目較大，傳統上用來設計一般IIR濾波器之二次式規畫法(quadratic programming)無法發揮功能。經實驗，當以二次式規畫法設計可調式分數延遲響應IIR數位濾波器，事實上可得到較現有方法為佳之結果，可是該法如脫韁之馬一般，無法收斂。在本計畫中，我們提出經改良之二次式規畫法，藉由加入適當之限制條件及目標誤差函數，非但可得到性能更好，且可快速收斂之結果，因此稱該法為“被馴服之二次式規畫法“。而實驗結果也顯示，應用該法設計可調式分數延遲響應IIR數位濾波器，可獲致約12 dB之誤差改善。由於本辦法首次被提出，相信另有諸多應用等待開發，此也將是本計畫之目標之一。
英文摘要：Recently, variable fractional-delay (VFD) digital filters are widely applied in signal processing and communications. Since the Farrow structure was proposed in 1988, several works for designing variable digital filters are presented including FIR-based design, allpass-based design and IIR-based design. Among of them, if the mean of group-delay is desirable smaller as much as possible, a VFD IIR filter is a preferred choice, which makes up the attractive features for VFD IIR filters. Because the number of coefficients for VFD IIR filters is generally huge, the conventional quadratic programming method, which is generally used to design stable 1-D IIR digital filters, can not be applied. Experiments show that comparing with the existing methods better performance can be obtained when the conventional quadratic programming method is adopted to design VFD IIR filters; but the method can not converge and just likes a runaway horse. In this project, a modified quadratic programming method is proposed. By incorporating appropriate constrained conditions and objective error functions, not only the performance of the designed VFD IIR filters is much better, but also the method can converge fast. Therefore, the proposed method is named by “a tamed quadratic programming method.“ By several simulations, it is shown that about 12 dB improvement for certain error criterion can be achieved. Due to the proposed method has not been presented in the existing literature, it is believed that several potential applications of the tamed quadratic programming method can be expected which will be probed into in this project, too.