Gamma Splines and Wavelets | Zendy

H. Olkkonen | Zendy; Juuso Olkkonen | Zendy

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Gamma Splines and Wavelets

Author(s) -

H. Olkkonen,

Juuso Olkkonen

Publication year - 2013

Publication title -

journal of engineering

Language(s) - English

Resource type - Journals

eISSN - 2314-4912

pISSN - 2314-4904

DOI - 10.1155/2013/625364

Subject(s) - wavelet , spline (mechanical) , convolution (computer science) , signal processing , algorithm , mathematics , impulse (physics) , impulse response , spline interpolation , multiresolution analysis , computer science , wavelet transform , bilinear interpolation , mathematical analysis , artificial intelligence , discrete wavelet transform , digital signal processing , statistics , artificial neural network , engineering , physics , quantum mechanics , computer hardware , structural engineering

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

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