Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement

Measurement Science Review

Li Yuanlu¹  Chen Haixiu¹  Meng Xiao²  Ding Yaqing²  Pan Chang² 

[1] B-DAT, School of Information and Control, Nanjing University of Information Science & Technology, Nanjing, China, 210044;Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing, China, 210044;

关键词: haar wavelet;    non–integer order calculus;    operational matrix;    signal enhancement;   

DOI  :  10.1515/msr-2015-0015

来源: DOAJ

【 摘 要 】

Non–integer order differentiation is changing application of traditional differentiation because it can achieve a continuous interpolation of the integer order differentiation. However, implementation of the non–integer order differentiation is much more complex than that of integer order differentiation. For this purpose, a Haar wavelet-based implementation method of non–integer order differentiation is proposed. The basic idea of the proposed method is to use the operational matrix to compute the non–integer order differentiation of a signal through expanding the signal by the Haar wavelets and constructing Haar wavelet operational matrix of the non–integer order differentiation. The effectiveness of the proposed method was verified by comparison of theoretical results and those obtained by another non–integer order differential filtering method. Finally, non–integer order differentiation was applied to enhance signal.

【 授权许可】

Unknown