Gamma Splines and Wavelets
In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation a...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Engineering |
| Online Access: | http://dx.doi.org/10.1155/2013/625364 |
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| _version_ | 1832555958589456384 |
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| author | Hannu Olkkonen Juuso T. Olkkonen |
| author_facet | Hannu Olkkonen Juuso T. Olkkonen |
| author_sort | Hannu Olkkonen |
| collection | DOAJ |
| description | In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG). Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment. |
| format | Article |
| id | doaj-art-d3414392798f43abbb6a3f14a57714d0 |
| institution | Kabale University |
| issn | 2314-4904 2314-4912 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Engineering |
| spelling | doaj-art-d3414392798f43abbb6a3f14a57714d02025-02-03T05:46:45ZengWileyJournal of Engineering2314-49042314-49122013-01-01201310.1155/2013/625364625364Gamma Splines and WaveletsHannu Olkkonen0Juuso T. Olkkonen1Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, FinlandVTT Technical Research Centre of Finland, 02044 Espoo, FinlandIn this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG). Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.http://dx.doi.org/10.1155/2013/625364 |
| spellingShingle | Hannu Olkkonen Juuso T. Olkkonen Gamma Splines and Wavelets Journal of Engineering |
| title | Gamma Splines and Wavelets |
| title_full | Gamma Splines and Wavelets |
| title_fullStr | Gamma Splines and Wavelets |
| title_full_unstemmed | Gamma Splines and Wavelets |
| title_short | Gamma Splines and Wavelets |
| title_sort | gamma splines and wavelets |
| url | http://dx.doi.org/10.1155/2013/625364 |
| work_keys_str_mv | AT hannuolkkonen gammasplinesandwavelets AT juusotolkkonen gammasplinesandwavelets |