njit-etd2003-081 - New Jersey Institute of Technology

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177 different values of A, over the length of f(x), the signals are multiplied, and the area under the product of the two signals is computed. If the cross-correlation function is normalized by the product of the square root of the auto cross-correlation of each function, then the normalized cross correlation will have a range from 0 to 1. For two signals that are the same, the cross-correlation at zero lag (when A= 0) is equal to 1. The closer the cross-correlation value is to 1, the more similar the waveforms are to one another. It should be pointed out that the power spectra (Fourier and wavelets) in this study are not continuous, but discrete. Therefore, to compute the discrete cross-correlation, the following equation was used [26]: where N is the number of points in the signal. To compute the cross-correlations for this section, a Matlab program was written and is listed in Appendix B. Based on the cross-correlation method presented, the cross-correlation coefficient between the Fourier power spectrum and the wavelet power spectrum was calculated for each COPD subject. Table 5.1 tabulates the cross-correlation results. It should be noted that the table displays the maximum absolute value of the cross-correlation function. From the table and the graph in figure 5.17, the values are from 0.2 to over 0.9 but all values indicated that the Morlet wavelet is the best representation.
178 Table 5.1 Correlation Indices of Wavelet Representations Subject Wigner Morl Meyer dB4 Mex Hat Haar 1 0.551 0.655 0.625 0.613 0.443 0.436 2 0.532 0.864 0.845 0.725 0.523 0.441 3 0.189 0.690 0.600 0.662 0.659 0.484 4 0.577 0.926 0.841 0.797 0.579 0.483 5 0.571 0.733 0.661 0.676 0.434 0.479 6 0.524 0.857 0.789 0.611 0.430 0.466 7 0.487 0.661 0.516 0.516 0.500 0.665 8 0.438 0.720 0.537 0.684 0.221 0.211 9 0.357 0.547 0.521 0.259 0.222 0.222 10 0.532 0.864 0.845 0.725 0.523 0.441 11 0.189 0.690 0.600 0.662 0.659 0.484 12 0.551 0.655 0.625 0.613 0.314 0.211 13 0.577 0.917 0.865 0.711 0.579 0.408 14 0.537 0.760 0.681 0.686 0.434 0.491 15 0.544 0.840 0.793 0.616 0.432 0.485 16 0.476 0.661 0.516 0.516 0.500 0.665 17 0.348 0.820 0.737 0.684 0.221 0.211 18 0.395 0.550 0.523 0.256 0.200 0.222 19 0.524 0.875 0.835 0.755 0.593 0.461 20 0.352 0.852 0.640 0.780 0.635 0.408 21 0.593 0.682 0.652 0.599 0.229 0.109 22 0.554 0.921_ 0.866 0.556 0.627 0.425 23 0.463 0.698 0.609 0.627 0.504 0.593 24 0.461 0.697 0.688 0.659 0.531 0.544 25 0.492 0.686 0.629 0.727 0.305 0.339 26 0.399 0.861 0.755 0.623 0.167 0.214 27 0.548 0.820 0.662 0.267 0.261 0.195 28 0.531 0.865 0.836 0.691 0.520 0.411 29 0.260 0.892 0.600 0.702 0.682 0.478 30 0.573 0.918 0.865 0.502 0.581 0.409 31 0.613 0.765 0.661 0.641 0.436 0.517
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Copyright Warning & Restrictions Th
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ABSTRACT TIME-FREQUENCY INVESTIGATI
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TIME-FREQUENCY INVESTIGATION OF HEA
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APPROVAL PAGE TIME-FREQUENCY INVEST
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BIOGRAPHICAL SKETCH (Continued) D.A
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ACKNOWLEDGMENT The author wishes to
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TABLE OF CONTENTS Chapter Page 1 IN
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TABLE OF CONTENTS (Continued) Chapt
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LIST OF FIGURES Figure Page 2.1 The
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LIST OF FIGURES (Continued) Figure
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LIST OF FIGURES (Continued) Figure
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ABBREVIATIONS A ABP Arterial Blood
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ABBREVIATIONS (Continued) P PID Pro
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2 mortality and sudden death. [2] B
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4 1) Patients with severe pulmonary
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6 examined for determining the inte
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8 identified using principal compon
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1 0 1. Present the application of t
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12 1.3 Outline of the Dissertation
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CHAPTER 2 PHYSIOLOGY BACKGROUND Bio
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16 Figure 2.2 The systemic and pulm
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18 illustrated in Figure 2.3. The i
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20 2.2 Blood Pressure The force tha
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22 2.4 The Nervous System Human beh
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24 The sympathetic nerve fibers lea
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26 Without these sympathetic and pa
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28 center in the medulla, which con
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30 Figure 2.6 Autonomic innervation
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32 average heart rate was measured
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34 However, they do note that there
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Figure 2.9 The placement of the pos
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38 female. While more men suffer fr
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40 Stage II: Moderate COPD - Worsen
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CHAPTER 3 ENGINEERING BACKGROUND Th
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44 Two common types of time-frequen
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46 STFT: Short-Time Fourier Transfo
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48 3.3 The Analytic Signal and Inst
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50 The advantage of using equation
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52 3.5 Covariance and Invariance Th
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where H(f), S(f) are Fourier transf
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56 Another shortcoming of the spect
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58 should take the kernel of the WD
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60 called the cross Wigner distribu
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62 3.6.3 The Choi-Williams (Exponen
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64 Figure 3.3 Performance of the Ch
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66 [-Ω,Ω ], then its STFT will be
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68 This condition forces that the w
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70 where c is a constant. Thus, the
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Figure 3.5 The time-frequency plane
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74 The measure dadb used in the tra
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76 and the wavelet transform repres
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78 Figure 3.6 Figure depicting the
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80 The final step to obtain the pow
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82 It should be noted that if the w
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84 The normal respiration rate can
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Figure 3.12 Power spectrum of BP II
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RR similar manner to give: When com
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90 when there is significant correl
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92 3.12 Partial Coherence Analysis
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94 after removal of the effects of
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96 The bulk of the theory and appli
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98 technique is measurement time. T
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100 usually attainable. The key poi
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102 variability exists in the propa
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104 eXogenous input (ARX) was used
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106 The baroreflex, an autonomic re
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108 the principal components are no
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110 The mathematical solution for t
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112 3.15 Cluster Analysis The term
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114 formed) one can read off the cr
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116 3.15.5 Squared Euclidian Distan
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118 Alternatively, one may use the
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120 Sneath and Sokal used the abbre
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122 may seem a bit confusing at fir
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CHAPTER 4 METHODS The purpose of th
Page 155 and 156: 126 4.1.2.1 Autonomic Testing. HR V
Page 157 and 158: 128 of heart rate, blood pressure,
Page 159 and 160: 130 The patients who underwent LVRS
Page 161 and 162: 132 panel of the Correct.vi. It was
Page 163 and 164: 134 4.2.3 Power Spectrum Analysis o
Page 165 and 166: 136 weighted-average value of the c
Page 167 and 168: 138 For each given scale a within t
Page 169 and 170: 140 frequency F to the wavelet func
Page 171 and 172: 142 4.2.8 System Identification Ana
Page 173 and 174: 144 In this study a simpler approac
Page 175 and 176: 146 Table 4.2 Parameters That Make
Page 177 and 178: 148 4.2.11 Cluster Analysis The sam
Page 179 and 180: 150 viewing the time series of sequ
Page 181 and 182: Figure 5.2 BPV analysis of a COPD s
Page 183 and 184: Figure 5.3 HRV analysis of a normal
Page 185 and 186: Figure 5.4.1 Comparison of the HRV
Page 187 and 188: 158 5.2 Time Frequency Analysis One
Page 189 and 190: Figure 5.5 Test signal with 3 sine
Page 191 and 192: 162 Figure 5.6 (c) CWD of a signal
Page 193 and 194: 164 Figure 5.7 (c) WT (dB4 wavelet)
Page 195 and 196: 166 HRV more information about HRV
Page 197 and 198: 168 Figure 5.9 (c) CWD plots of a n
Page 199 and 200: Figure 5.10 CWT (Morlet) HRV plot o
Page 201 and 202: 172 The following figures show the
Page 203 and 204: 174 Figure 5.15 CWT (Mexican Hat) H
Page 205: 176 5.2.5 Best Wavelet Selection fo
Page 209 and 210: 180 5.2.6 Vagal Tone and Sympathova
Page 211 and 212: 182 These figures basically show th
Page 213 and 214: 184 Figure 5.20 Sympathetic and par
Page 217 and 218: 188 5.2.7 Time-Frequency Analysis (
Page 219 and 220: 190 Figure 5.29 3D and contour plot
Page 221 and 222: 192 Figure 5.33 3D and contour plot
Page 229 and 230: Figure 5.44 Plot of raw respiration
Page 231 and 232: Figure 5.46 The LF partial coherenc
Page 233 and 234: Figure 5.48 HF partial coherence pl
Page 235 and 236: Table 5.2 Cross-Spectral Analysis o
Page 237 and 238: Table 5.3 Cross-Spectral Analysis o
Page 239 and 240: Figure 5.50 HF coherence of COPD (1
Page 241 and 242: 212 For better presentation of the
Page 243 and 244: Figure 5.53 Coherence and partial c
Page 245 and 246: 216 2. Interpretation of the transf
Page 247 and 248: 218 covariances of the parameters,
Page 249 and 250: 220 deviations are interpreted as A
Page 251 and 252: 222 Figure 5.58 Bode plot of the HR
Page 253 and 254: 224 In this section a simple model
Page 255 and 256: 226 The data for all 47 COPD subjec
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228 Figure 5.60 Normal and COPD cla
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230 Figure 5.61 Normal and COPD cla
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232 Figure 5.62 Normal classificati
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234 5.7 Cluster Analysis The purpos
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236 Figure 5.64 Severity classifica
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238 both the normal and COPD subjec
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240 In summary, COPD subjects had h
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APPENDIX A EXERCISE PHYSIOLOGY A.1
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244 A.3 Figure Out Your Target Hear
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APPENDIX B ANALYSIS PROGRAM LISTING
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248 4) Click on file, close to exit
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250 • TN 11
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252 B.1.2 Partial Coherence Between
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254
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256 Block Diagram !rime of record K
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258
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260 B.2.2 Time — Frequency Analys
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262 This program provides the STFT
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264 G(:j+1)=G(:,j+1)/(2*sum(G(:j+1)
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266 T=(length(Signa)/sample)/(Times
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268 subplot(3, 1,3), plot(T,E); xla
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270 4. The program creates five out
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272 B.2.3.4 Program to Generate Sym
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274 ylabel('frequency'); title('Ins
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276 The program will run and output
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278 axis([0 1 0 2]); grid on; xlabe
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280 vagal=sum(TFDs(HFC,1:k)); symto
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282 plot(J,symtopar); %plot(A,symto
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284 4. Remove the constant levels a
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286 Make sure the agreement is quit
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288 B.2.6 Principal Components Anal
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290 Columns 12 through 15 'LF_pcoh_
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292 I= 1.0000 -0.0000 -0.0000 -0.00
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294 variances = 3.4083 1.2140 1.141
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296 B.2.7 Cluster Analysis Program
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298 end [R,C]=size(Data); if length
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300 B.2.8 Cross-correlation Program
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302 C.3 Partial coherence of HR and
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304 [13] Madwed, J., and R. Cohen.
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306 [41] Mallat, S. G., "A Theory f
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[70] Tazebay, M.V., R.T. Saliba and
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