四川大学学报（自然科学版）2025，Vol.62Issue(2)：425-432,8.DOI:10.19907/j.0490-6756.240001
理想的分数阶数字微分器系数的解析表示
Analysis representation of the coefficients of an ideal fractional-order digital differentiator
摘要
Abstract
This paper demonstrates that the coefficients of an ideal fractional-order digital differentiator are equal to the values of the fractional-order derivatives of the Sinc function at integer points.The coefficients of the ideal fractional-order digital differentiator and the fractional-order derivatives of the Sinc function are repre-sented using the incomplete gamma function and the hypergeometric function,respectively.Based on the defi-nition and properties of the incomplete gamma function,the analytical representation of the coefficients of the ideal fractional-order digital differentiator is theoretically derived.Furthermore,by utilizing the Taylor series expansion of sine and cosine functions and the definition of the hypergeometric function,the hypergeometric function representation of the coefficients of the ideal fractional-order digital differentiator is theoretically de-rived.The feasibility of accurately representing the coefficients of the ideal fractional-order digital differentia-tor and the fractional-order derivatives of the Sinc function using the incomplete gamma function and the hy-pergeometric function is verified by comparison with high-precision numerical algorithm results for the fractional-order derivatives of the Sinc function.关键词
分数阶微积分/单位冲激响应/Sinc函数/不完全伽马函数/超几何函数/解析表示Key words
Fractional-order calculus/Unit impulse response/Sinc function/Incomplete Gamma function/Hypergeometric function/Analysis representation分类
信息技术与安全科学引用本文复制引用
杨劲松,杨紫怡,袁晓..理想的分数阶数字微分器系数的解析表示[J].四川大学学报（自然科学版）,2025,62(2):425-432,8.基金项目
国家自然科学基金(62171303) （62171303）
