分数阶微分Whittaker平滑器

目前Whittaker Smoother(WS)算法应用广泛,该算法的核心在于用整数阶微分来表示粗糙度.但整数阶微分表示过于单一,不够灵活,不能真实反映出信号的粗糙度.相反分数阶微分表示丰富,可以更好地描述真实信号的粗糙度.因此,本文用分数阶微分来改进WS算法,使它更加灵活有效.采用Riemann-Liouvile(RL)和Grumwald-Letnikov(GL)两种不同的分数阶微分计算方法来实现分数阶WS算法.此外,通过数学推导,实现分数阶WS算法的自动选参.含有尖锐峰的核磁共振谱实验结果表明:分数阶WS算法可以提取更多的真实信息;Marzipan红外光谱实验结果表明:与原有整数阶WS算法相比,光谱定量分析的精度更高.

Fractional Differential Whittaker Smoother

At present, the Whittaker Smoother(WS)algorithm is widely used. The core of the algorithm lies in the use of integer-order differentiation to express roughness. However, the integer-order differential representation is single and not flexible enough to truly reflect the roughness of the signal. On the contrary, the fractional differential expression is flexible and can better describe the roughness of the real signal. Therefore, the fractional differentiation is used to improve the WS algorithm and make it more flexible and effective. As two fractional differential calculation methods, Riemann-Liouville(RL)and Grümwald-Letnikov(GL)are adopted to implement the fractional WS algorithm.Furthermore, the automatic parameter selection of the fractional WS algorithm is realized by mathematical derivation. The experimental results of the nuclear magnetic resonance spectrum with sharp peaks show that the fractional-order WS algorithm can extract more real information; additionally, the experimental results of Marzipan infrared spectra show that the precision of spectral quantitative analysis is higher compared with the original integer-order WS algorithm.