Wavelet basis functions in biomedical signal processing - SPAN LAB

J. Rafiee et al. / Expert Systems with Applications 38 (2011) 6190–6201 619320 Normal (Neutral)151000.025 (Neutral)1055005050.08 (Neutral)60Normal (Erotic)20040100200805050.025 (Erotic)0.08 (Erotic)604040202005(Hz)05(Hz)Fig. 5. Power spectrum density (V 2 /Hz) of VPA recorded in six classes (one specific subject).The CWT results in continuous wavelet coefficients (CWC),which illustrate how well a wavelet function correlates with a specificsignal. If the signal has a major frequency component correspondingto a particular scale, then the wavelet at this scale issimilar to the signal at the location where this frequency componentoccurs, regardless of its amplitudes and phases. Correlationis one of the most common statistical measures, and describesthe degree of linear dependence between two variables in termsof a coefficient between 1 and +1. The closer the coefficient isto either 1 or +1, the stronger the correlation between the twovariables. The negative or positive sign of the coefficient indicatesthe direction of the linear dependence. The coefficient 0 impliesthat the two variables are completely linearly independent of eachother. q x,y , the correlation between two random variables x and ywith expected values l x and l y and standard deviations r x andr y is defined as:covðx; yÞq x;y¼ ¼ Eððx l x Þðy l y ÞÞ; ð3Þr x r y r x r ywhere E stands for expected value of the variable and cov stands forcovariance. As E(x)=l x , E(y)=l y and r 2 (x)=E(x 2 ) E 2 (x),r 2 (y)=E(y 2 ) E 2 (y), q x,y can be defined as:EðxyÞ EðxÞEðyÞq x;y¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEðx 2 Þ E 2 ðxÞ Eðy 2 Þ E 2 ðyÞIn this research, the outcome of the correlation between signaland wavelet basis function (CWC) has been established as the basisfor comparing selected mother wavelet functions. Consequently,ð4Þto find the most similar mother wavelet to biosignals, motherwavelets from different families including Haar, Daubechies (db),Symlet, Coiflet, Gaussian, Morlet, complex Morlet, Mexican hat,bio-orthogonal, reverse bio-orthogonal, Meyer, discrete approximationof Meyer, complex Gaussian, Shannon, and frequency B-splinefamilies have been analyzed based on CWC and using the followingalgorithm:1. Signal segmentation: EMG, EEG, VPA signals were segmented tothe 256-points, 500-points, 960-points (12 s) windows, respectivelyas shown in Figs. 6 and 7 for EMG and VPA.2. One class of recorded data is selected from one channel for onesubject for each type of biosignal. The number of subjects is 20,6, and 1 for VPA, EMG, and EEG, respectively. There are 1, 16, 6,and 3 channels for recording the signals for VPA, surface EMG,intramuscular EMG, and EEG, respectively.3. One mother wavelet function is selected from 324 candidates.In the fourth decomposition level, CWC of the segmented signalswere calculated (2 4 numbers for each segmented signal).4. Absolute value of CWC in each scale (2 4 scales) was determinedusing 324 mother wavelets in a segmented signal for each of the10 hand motions for EMG, as well as each of three specific channelsfor EEG. Next, the sum of this value in all 2 4 scales wasdetermined for 20 EMG segmented signals (signals with thelength of 256 points), 50 EEG segmented signals (signals withthe length of 500 points), and 15 VPA segmented signals (signalswith the length of 960 points). Their average was calculatedfor each type of signal and called the evaluationcriterion (EC) for simplicity and to find the most similar mother