提出了一種理想數(shù)字分數(shù)微分器系數(shù)的快速算法。從理想數(shù)字分數(shù)微分器系數(shù)計算公式的特點考慮，利用變量代換把積分函數(shù)中的振蕩因子轉換成積分上限，避免高階振蕩函數(shù)積分計算，給出了計算分數(shù)微分器系數(shù)的遞推公式。分析了快速算法的計算復雜度、穩(wěn)定性和收斂性等問題。實驗結果表明新算法具有運算量少，運算速度快并具有較好的穩(wěn)定性和收斂性。
關 鍵 詞 分數(shù)微分器; 振蕩因子; 快速算法; 穩(wěn)定性

Abstract A new fast algorithm for calculating the coefficients of ideal digital fractional differentiator is presented. It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function. Based on the properties of the integral formula, it’s easy to convert the oscillating factor to the integral upper limit. Therefore a set of recursive expressions for calculating coefficients of ideal digital fractional differentiator are introduced in this paper. The experimental result shows that the new algorithm decreases the amount of operation greatly, at the same time promotes the algorithm’s efficiency as well as avoid integral of high-order oscillating function.
Key words digital fractional differentiator; oscillating factor; fast algorithm; stability