Wavelet basis functions in biomedical signal processing - SPAN LAB

J. Rafiee et al. / Expert Systems with Applications 38 (2011) 6190–6201 6197db44Channel 1900880Evaluation Criterionx 10 62db44db44Channel 2Channel 3Evaluation Criterion860840660640620Db44 & Db45HaarForearm Pronation5 10 15 20 25 30 35 40 45HaarDb44 & Db45Spread Fingers15 10 15 20 25 30 35 40 4500 50 100 150 200 250 300Mother wavelet functionsFig. 13. Trend of Daubechies family vs. evaluation criterion in Intramuscular EMGsignals for two motions.Fig. 11. Evaluation criterion (no unit) across 324 mother wavelet candidates forEEG signals across three channels (Pz, POz, Oz).Evaluation Criterion21.510.5x 10 7db45Haardb44shan0.2-0.1shan0.1-0.1cmor3-0.1cmor4-0.1fbsp1-0.1-0.1shan0.5-0.1fbsp3-0.1-0.1fbsp2-0.1-0.1fbsp1-0.2-0.1fbsp2-0.2-0.1fbsp3-0.2-0.1bior3.1gaus1cgau1rbio3.1Evaluation Criterion80007000600050004000300020001000db45db44cmor1-0.01two motionsshan0.2-0.1dmeymeyrcmor1-0.1cmor4-0.1shan0.5-0.1fbsp1-0.2-0.1shan5-0.2shan1-0.4 fbsp3-0.2-0.9fbsp3-0.2-0.1fbsp2-0.2-0.1fbsp1-0.2-0.2cmor1-1.5fbsp3-0.1-0.1rbio5-5fbsp2-0.1-0.1fbsp1-0.1-0.1 bior3-100 50 100 150 200 250 300Mother wavelet functionsFig. 12. Evaluation criterion (no unit) vs. mother wavelets for VPA signals recordedfrom one subject.Intramuscular EMG signals. As shown, the EC increases slightly inlow-order db and decreases slightly for high-order db. This demonstratesthat Daubechies functions do not behave dramatically differenton the biosignals, while ranging from db1 to db43. It alsohighlights the likely limitation of the mostly lower order Daubechiesthat typically are used in prior research. The trend changesdramatically for db44, which cannot be seen in Fig. 13 due to scalingrestrictions.db44 and db45 are the most similar functions as the other 322functions have pronouncedly poorer performance (similarity).Closer examination of the evaluation criterion (see Figs. 12 and14) for VPA and intramuscular EMG reveals some variability of fitamongst other function families. To demonstrate the difference betweendb44 and the other functions, the continuous wavelet coefficientsof one of the segmented unit signals using db44 has been0Mother wavelet functionsFig. 14. Evaluation criterion (no unit) vs. mother wavelets for intramuscular EMGsignals recorded from one of the six channels of data acquisition system.compared to those calculated with the Morlet function, whichhas been used frequently in previous research (see Figs. 15 and16, see Fig. 17 for decomposition scale) (e.g. Saravanan, KumarSiddabattuni, & Ramachandran, 2008). The difference betweenthe values of the CWC (Y-axis) calculated by db44 is much higherthan those calculated by Morlet function. Moreover, periodic sinusoidaltrends also are obvious using the db44. This is a very desirablefeature, because it means that periodic behavior can beextracted from biological signals using db44 function. This mightbe useful for preprocessing biological signals.Some other complex mother wavelets (in addition to db44 anddb45) show high similarity to EEG and VPA signals (e.g. see Fig. 12).After db44 and db45, EEG signals also display some similarity tobior 3.1 and other complex mother wavelets unlike the EMG. However,these differences appear minor and appear due mostly tocomplex functions with different wavelet center frequency. Thecenter frequency varies simply with the frequency contents ofthe signals.