Wavelet basis functions in biomedical signal processing - SPAN LAB

J. Rafiee et al. / Expert Systems with Applications 38 (2011) 6190–6201 6195Raw biosignals(selected class)Segmentation of signals into smaller units for each subjectSegmented signals foreach six class324 motherwavelet functionsSelecting a mother wavelet and one segmented signal from one class andfrom one specific subjectS= sum of absolute value of CWC in all scales for eachsegmented signal and for each classAS= average of S insegmented samplesEC= average of AS forsubjectsEC Max inclass 1EC Max inclass 2EC Max inclass 3EC Max inclass 4EC Max inclass NMother wavelet for each classFig. 8. Searching algorithm to find the most similar mother wavelet based on evaluation criterion (for biosignals). R 11 w rðxÞdx ¼ R 11 xr w r ðxÞdx ¼ 0.Daubechies’ wavelets provide appropriate results in signal processingtechniques due to the above-mentioned properties. Awavelet function with compact support can be implemented easilyby finite length filters. Moreover, the compact support enables spatialdomain localization. Since the wavelet basis functions havecontinuous derivatives, they decompose a continuous functionmore efficiently while avoiding edge artifacts. Since the motherwavelets are used to characterize details in a signal, they shouldhave a zero integral so that the trend information is stored in thecoefficients obtained by the father wavelet. A Daubechies’ waveletrepresentation of a function is a linear combination of the waveletbasis functions. Daubechies’ wavelet transforms are usually implementednumerically via quadratic mirror filters. Multiresolutionanalysis of the trend and fluctuation of a function is implementedby convolving it with a low-pass filter and a high-pass filter thatare versions of the same wavelet.As shown in biosignals, the signal with a sharp spike is properlyanalyzed by Daubechies’ wavelets, because much less energy (ortrend) is stored in the high-pass bands. Hence, Daubechies’ waveletsare ideally suited for natural signals. In general, Daubechies’wavelets with long-length filters give more appropriate energyconcentration than those with short-length filters. Therefore, thementioned reason supports the use of EC to find the most similarfunction to biosignals. Besides, as illustrated in Fig. 9, db44 is theonly Daubechies function with near-symmetric characteristic aswell as having sharp spike that would be matched with naturalsignals.4. Results and discussionThe result shows that, among all wavelet families considered inTables 1A–2B (Appendix A), Daubechies 44 (db 44) provides a betterfit to the tested biosignals. Figs. 10–12 show the EC acrossmother wavelet candidates for surface EMG, EEG, and VPA signals,respectively. For example, in Fig. 10, all classes of EMG (for 10 differenthand motions) have a peak whose amplitude is greater thanthose calculated by the other candidate mother wavelets. The peakrepresents the largest EC which is calculated by db44. The samepattern was achieved for other biosignals. The difference betweendb44 and the other 323 wavelet functions towards biosignals is