<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

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

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Non–integer order differentiation is changing application of traditional differentiation because it can achieve a continuous interpolation of the integer order...

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

Published Online: Jul 10, 2015

Page range: 101 - 106

Received: Nov 18, 2014

Accepted: Jun 18, 2015

DOI: https://doi.org/10.1515/msr-2015-0015

Keywords
Haar wavelet, non–integer order calculus, operational matrix, signal enhancement

© Yuanlu Li et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Jul 10, 2015

Page range: 101 - 106

Received: Nov 18, 2014

Accepted: Jun 18, 2015

DOI: https://doi.org/10.1515/msr-2015-0015

KeywordsHaar wavelet, non–integer order calculus, operational matrix, signal enhancement

© Yuanlu Li et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Haar wavelet, non–integer order calculus, operational matrix, signal enhancement