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Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement
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| Zeitschriftentitel: | Measurement Science Review |
|---|---|
| Personen und Körperschaften: | , , , , |
| In: | Measurement Science Review, 15, 2015, 3, S. 101-106 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Walter de Gruyter GmbH
|
| Schlagwörter: |
| author_facet |
Li, Yuanlu Pan, Chang Meng, Xiao Ding, Yaqing Chen, Haixiu Li, Yuanlu Pan, Chang Meng, Xiao Ding, Yaqing Chen, Haixiu |
|---|---|
| author |
Li, Yuanlu Pan, Chang Meng, Xiao Ding, Yaqing Chen, Haixiu |
| spellingShingle |
Li, Yuanlu Pan, Chang Meng, Xiao Ding, Yaqing Chen, Haixiu Measurement Science Review Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement Instrumentation Biomedical Engineering Control and Systems Engineering |
| author_sort |
li, yuanlu |
| spelling |
Li, Yuanlu Pan, Chang Meng, Xiao Ding, Yaqing Chen, Haixiu 1335-8871 Walter de Gruyter GmbH Instrumentation Biomedical Engineering Control and Systems Engineering http://dx.doi.org/10.1515/msr-2015-0015 <jats:title>Abstract</jats:title> <jats: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.</jats:p> Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement Measurement Science Review |
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| title |
Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_unstemmed |
Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_full |
Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_fullStr |
Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_full_unstemmed |
Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_short |
Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_sort |
haar wavelet based implementation method of the non–integer order differentiation and its application to signal enhancement |
| topic |
Instrumentation Biomedical Engineering Control and Systems Engineering |
| url |
http://dx.doi.org/10.1515/msr-2015-0015 |
| publishDate |
2015 |
| physical |
101-106 |
| description |
<jats:title>Abstract</jats:title>
<jats: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.</jats:p> |
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| author | Li, Yuanlu, Pan, Chang, Meng, Xiao, Ding, Yaqing, Chen, Haixiu |
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| description | <jats:title>Abstract</jats:title> <jats: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.</jats:p> |
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| physical | 101-106 |
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| series | Measurement Science Review |
| source_id | 49 |
| spelling | Li, Yuanlu Pan, Chang Meng, Xiao Ding, Yaqing Chen, Haixiu 1335-8871 Walter de Gruyter GmbH Instrumentation Biomedical Engineering Control and Systems Engineering http://dx.doi.org/10.1515/msr-2015-0015 <jats:title>Abstract</jats:title> <jats: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.</jats:p> Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement Measurement Science Review |
| spellingShingle | Li, Yuanlu, Pan, Chang, Meng, Xiao, Ding, Yaqing, Chen, Haixiu, Measurement Science Review, Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement, Instrumentation, Biomedical Engineering, Control and Systems Engineering |
| title | Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_full | Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_fullStr | Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_full_unstemmed | Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_short | Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| title_sort | haar wavelet based implementation method of the non–integer order differentiation and its application to signal enhancement |
| title_unstemmed | Haar Wavelet Based Implementation Method of the Non–integer Order Differentiation and its Application to Signal Enhancement |
| topic | Instrumentation, Biomedical Engineering, Control and Systems Engineering |
| url | http://dx.doi.org/10.1515/msr-2015-0015 |