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 gm,b(t)=tme-bt, t≥0 are born by (m+1)-times convolution of the exponential e-bt 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.