Wavelet basis functions in biomedical signal processing - SPAN LAB

J. Rafiee et al. / Expert Systems with Applications 38 (2011) 6190–6201 6199Table 1AStudied wavelet families in this research (Rafiee et al., 2010).No. Family (short form) Order1 Haar (db1) db 12–45 Daubechies(db) db 2–db 4546–50 Coiflet (coif) coif 1–coif 551 Morlet (Morl) morl52–147 Complex Morlet (cmor Fb-Fc) a Included Table 1B148 Discrete Meyer (dmey) dmey149 Meyer (meyr) meyr150 Mexican Hat (mexh) mexh151–200 Shannon (Shan Fb-Fc) a Included Table 1B201–260 Frequency B-Spline (fbsp M-Fb- Fc) a Included Table 1B261–267 Gaussian (gaus) gaus 1–gaus 7268–275 Complex Gaussian (cgau) cgau 1–cgau 8276–290 Biorthogonal (bior Nr.Nd) b Included Table 1B291–305 Reverse Biorthogonal (rbio Nr.Nd) b Included Table 1B306–324 Symlet (sym) sym 2–sym 20aFb is a bandwidth parameter, Fc is a wavelet center frequency, and M is aninteger order parameter.b Nr and Nd are orders: r for reconstruction/d for decomposition.5. ConclusionsIn summary, db44 appears to be the most similar function toEMG, EEG, and VPA signals among 324 mother wavelet functions.Symmetric mother wavelets have been shown more proper resultswith biosignals in prior research. Daubechies are orthogonal compactsupport functions and are not symmetric. However, db44 possessesa near-symmetric attribute (see Fig. 9) that well-matchedthe biosignals. Most biosignals possess sharp spikes that could beappropriately analyzed using Daubechies’ wavelets to reflect sharp,asymmetric spikes seen in these signals. These features of db44suggest that it would be effective for many biosignal processingmethods based on the resemblance of the signal and mother waveletfunction.The similarity between signal and mother wavelet function isnot always proper for signal processing based on wavelet transformand it is just appropriate for those wavelet-based processingmethods based on the resemblance between signals and motherfunctions.Table 1BStudied wavelet families in detail (Rafiee et al., 2010).No Wave No Wave No Wave No Wave No Wave52 1–1.5 100 3–1.1 148 dmey 196 2–0.6 244 2–0.2–0.453 1–1 101 3–1.2 149 meyr 197 2–0.7 245 2–0.2–0.554 1–0.5 102 3–1.3 150 mexh 198 2–0.8 246 2–0.2–0.655 1–0.3 103 3–1.4 151 0.1–0.1 199 2–0.9 247 2–0.2–0.756 1–0.2 104 3–1.5 152 0.1–0.2 200 1–1 248 2–0.2–0.857 1–0.1 105 3–1.6 153 0.1–0.3 201 1–0.1–0.1 249 2–0.2–0.958 1–0.05 106 3–1.8 154 0.1–0.4 202 1–0.1–0.2 250 2–0.2–159 1–0.02 107 3–1.9 155 0.1–0.5 203 1–0.1–0.3 251 3–0.2–0.160 1–0.01 108 3–2 156 0.1–0.6 204 1–0.1–0.4 252 3–0.2–0.261 2–0.1 109 3–2.1 157 0.1–0.7 205 1–0.1–0.5 253 3–0.2–0.362 2–0.2 110 3–2.2 158 0.1–0.8 206 1–0.1–0.6 254 3–0.2–0.463 2–0.3 111 3–2.3 159 0.1–0.9 207 1–0.1–0.7 255 3–0.2–0.564 2–0.4 112 3–2.4 160 0.1–1 208 1–0.1–0.8 256 3–0.2–0.665 2–0.5 113 3–2.5 161 0.2–0.1 209 1–0.1–0.9 257 3–0.2–0.766 2–0.6 114 3–2.6 162 0.2–0.2 210 1–0.1–1 258 3–0.2–0.867 2–0.7 115 3–2.7 163 0.2–0.3 211 2–0.1–0.1 259 3–0.2–0.968 2–0.8 116 3–2.8 164 0.2–0.4 212 2–0.1–0.2 260 3–0.2–169 2–0.9 117 3–2.9 165 0.2–0.5 213 2–0.1–0.3 276 1.170 2–1 118 3–3 166 0.2–0.6 214 2–0.1–0.4 277 1.371 2–1.1 119 4–0.1 167 0.2–0.7 215 2–0.1–0.5 278 1.572 2–1.2 120 4–0.2 168 0.2–0.8 216 2–0.1–0.6 279 2.273 2–1.3 121 4–0.3 169 0.2–0.9 217 2–0.1–0.7 280 2.474 2–1.4 122 4–0.4 170 0.2–1 218 2–0.1–0.8 281 2.675 2–1.5 123 4–0.5 171 0.5–0.1 219 2–0.1–0.9 282 2.876 2–1.6 124 4–0.6 172 0.5–0.2 220 2–0.1–1 283 3.177 2–1.8 125 4–0.7 173 0.5–0.3 221 3–0.1–0.1 284 3.378 2–1.9 126 4–0.8 174 0.5–0.4 222 3–0.1–0.2 285 3.579 2–2 127 4–0.9 175 0.5–0.5 223 3–0.1–0.3 286 3.780 2–2.1 128 4–1 176 0.5–0.6 224 3–0.1–0.4 287 3.981 2–2.2 129 4–1.1 177 0.5–0.7 225 3–0.1–0.5 288 4.482 2–2.3 130 4–1.2 178 0.5–0.8 226 3–0.1–0.6 289 5.583 2–2.4 131 4–1.3 179 0.5–0.9 227 3–0.1–0.7 290 6.884 2–2.5 132 4–1.4 180 0.5–1 228 3–0.1–0.8 291 1.185 2–2.6 133 4–1.5 181 1–0.1 229 3–0.1–0.9 292 1.386 2–2.7 134 4–1.6 182 1–0.2 230 3–0.1–1 293 1.587 2–2.8 135 4–1.8 183 1–0.3 231 1–0.2–0.1 294 2.288 2–2.9 136 4–1.9 184 1–0.4 232 1–0.2–0.2 295 2.489 2–3 137 4–2 185 1–0.5 233 1–0.2–0.3 296 2.690 3–0.1 138 4–2.1 186 1–0.6 234 1–0.2–0.4 297 2.891 3–0.2 139 4–2.2 187 1–0.7 235 1–0.2–0.5 298 3.192 3–0.3 140 4–2.3 188 1–0.8 236 1–0.2–0.6 299 3.393 3–0.4 141 4–2.4 189 1–0.9 237 1–0.2–0.7 300 3.594 3–0.5 142 4–2.5 190 1–1 238 1–0.2–0.8 301 3.795 3–0.6 143 4–2.6 191 2–0.1 239 1–0.2–0.9 302 3.996 3–0.7 144 4–2.7 192 2–0.2 240 1–0.2–1 303 4.497 3–0.8 145 4–2.8 193 2–0.3 241 2–0.2–0.1 304 5.598 3–0.9 146 4–2.9 194 2–0.4 242 2–0.2–0.2 305 6.899 3–1 147 4–3 195 2–0.5 243 2–0.2–0.3