njit-etd2003-081 - New Jersey Institute of Technology

More documents

Recommendations

Info

59 One can therefore recover the original signal from the Wigner distribution for a given resolution. The preceding relation can be used to determine whether a signal exists which will generate a given ρw(t,f). The Wigner distribution also satisfies the marginals properties. To prove these, one can use the constraint of the kernel for marginals properties, that is: By inspection, the kernel of the Wigner distribution g(v, r) = 1 satisfies both marginals. Thus, the Wigner distribution satisfies the total energy. Note the converse is not true [38]. For the first conditional moment at a fixed time, the Wigner distribution gives the instantaneous frequency and at a fixed frequency the first conditional moment would be the group delay. For a finite duration signal, the Winger distribution is zero before the signal starts and after the signal ends [38]. If one have a band limited signal, the Wigner distribution will be zero for all frequencies that are not included in that band. These properties are called the support properties of the Wigner distribution. In general the Wigner distribution is not zero when the signal is zero [40]. Consider the multicomponent signal z(t): The Wigner distribution is:
60 called the cross Wigner distributions. Therefore the Wigner distribution of the sum of the two signals is not the sum of their respective Wigner distributions. In general the Wigner distribution puts cross terms in between any two frequencies and any two times [40]. Figure 3.2 The Wigner distribution of the sum of two finite duration sine waves. The figure above presents the Wigner distribution of a signal, which is the sum of two sine waves of one-second duration with frequencies of 100 and 400 hertz. Note the cross term in the middle of the two frequencies at 250 hertz. This is the most important draw back of the Wigner distribution (WD). Another draw back of the Wigner distribution is that it always has negative regions throughout the time-frequency plane, except in the case of the Gaussian signal where the amplitude is modulated [40].
Page 1 and 2:
Copyright Warning & Restrictions Th
Page 3 and 4:
ABSTRACT TIME-FREQUENCY INVESTIGATI
Page 5 and 6:
TIME-FREQUENCY INVESTIGATION OF HEA
Page 7 and 8:
APPROVAL PAGE TIME-FREQUENCY INVEST
Page 9 and 10:
BIOGRAPHICAL SKETCH (Continued) D.A
Page 11 and 12:
ACKNOWLEDGMENT The author wishes to
Page 13 and 14:
TABLE OF CONTENTS Chapter Page 1 IN
Page 15 and 16:
TABLE OF CONTENTS (Continued) Chapt
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
LIST OF FIGURES Figure Page 2.1 The
Page 23 and 24:
LIST OF FIGURES (Continued) Figure
Page 25 and 26:
LIST OF FIGURES (Continued) Figure
Page 27 and 28:
ABBREVIATIONS A ABP Arterial Blood
Page 29 and 30:
ABBREVIATIONS (Continued) P PID Pro
Page 31 and 32:
2 mortality and sudden death. [2] B
Page 33 and 34:
4 1) Patients with severe pulmonary
Page 35 and 36:
6 examined for determining the inte
Page 37 and 38: 8 identified using principal compon
Page 39 and 40: 1 0 1. Present the application of t
Page 41 and 42: 12 1.3 Outline of the Dissertation
Page 43 and 44: CHAPTER 2 PHYSIOLOGY BACKGROUND Bio
Page 45 and 46: 16 Figure 2.2 The systemic and pulm
Page 47 and 48: 18 illustrated in Figure 2.3. The i
Page 49 and 50: 20 2.2 Blood Pressure The force tha
Page 51 and 52: 22 2.4 The Nervous System Human beh
Page 53 and 54: 24 The sympathetic nerve fibers lea
Page 55 and 56: 26 Without these sympathetic and pa
Page 57 and 58: 28 center in the medulla, which con
Page 59 and 60: 30 Figure 2.6 Autonomic innervation
Page 61 and 62: 32 average heart rate was measured
Page 63 and 64: 34 However, they do note that there
Page 65 and 66: Figure 2.9 The placement of the pos
Page 67 and 68: 38 female. While more men suffer fr
Page 69 and 70: 40 Stage II: Moderate COPD - Worsen
Page 71 and 72: CHAPTER 3 ENGINEERING BACKGROUND Th
Page 73 and 74: 44 Two common types of time-frequen
Page 75 and 76: 46 STFT: Short-Time Fourier Transfo
Page 77 and 78: 48 3.3 The Analytic Signal and Inst
Page 79 and 80: 50 The advantage of using equation
Page 81 and 82: 52 3.5 Covariance and Invariance Th
Page 83 and 84: where H(f), S(f) are Fourier transf
Page 85 and 86: 56 Another shortcoming of the spect
Page 87: 58 should take the kernel of the WD
Page 91 and 92: 62 3.6.3 The Choi-Williams (Exponen
Page 93 and 94: 64 Figure 3.3 Performance of the Ch
Page 95 and 96: 66 [-Ω,Ω ], then its STFT will be
Page 97 and 98: 68 This condition forces that the w
Page 99 and 100: 70 where c is a constant. Thus, the
Page 101 and 102: Figure 3.5 The time-frequency plane
Page 103 and 104: 74 The measure dadb used in the tra
Page 105 and 106: 76 and the wavelet transform repres
Page 107 and 108: 78 Figure 3.6 Figure depicting the
Page 109 and 110: 80 The final step to obtain the pow
Page 111 and 112: 82 It should be noted that if the w
Page 113 and 114: 84 The normal respiration rate can
Page 115 and 116: Figure 3.12 Power spectrum of BP II
Page 117 and 118: RR similar manner to give: When com
Page 119 and 120: 90 when there is significant correl
Page 121 and 122: 92 3.12 Partial Coherence Analysis
Page 123 and 124: 94 after removal of the effects of
Page 125 and 126: 96 The bulk of the theory and appli
Page 127 and 128: 98 technique is measurement time. T
Page 129 and 130: 100 usually attainable. The key poi
Page 131 and 132: 102 variability exists in the propa
Page 133 and 134: 104 eXogenous input (ARX) was used
Page 135 and 136: 106 The baroreflex, an autonomic re
Page 137 and 138: 108 the principal components are no
Page 139 and 140:
110 The mathematical solution for t
Page 141 and 142:
112 3.15 Cluster Analysis The term
Page 143 and 144:
114 formed) one can read off the cr
Page 145 and 146:
116 3.15.5 Squared Euclidian Distan
Page 147 and 148:
118 Alternatively, one may use the
Page 149 and 150:
120 Sneath and Sokal used the abbre
Page 151 and 152:
122 may seem a bit confusing at fir
Page 153 and 154:
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 and 206:
176 5.2.5 Best Wavelet Selection fo
Page 207 and 208:
178 Table 5.1 Correlation Indices o
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 215 and 216:
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 223 and 224:
Page 225 and 226:
Page 227 and 228:
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
Page 257 and 258:
228 Figure 5.60 Normal and COPD cla
Page 259 and 260:
230 Figure 5.61 Normal and COPD cla
Page 261 and 262:
232 Figure 5.62 Normal classificati
Page 263 and 264:
234 5.7 Cluster Analysis The purpos
Page 265 and 266:
236 Figure 5.64 Severity classifica
Page 267 and 268:
238 both the normal and COPD subjec
Page 269 and 270:
240 In summary, COPD subjects had h
Page 271 and 272:
APPENDIX A EXERCISE PHYSIOLOGY A.1
Page 273 and 274:
244 A.3 Figure Out Your Target Hear
Page 275 and 276:
APPENDIX B ANALYSIS PROGRAM LISTING
Page 277 and 278:
248 4) Click on file, close to exit
Page 279 and 280:
250 • TN 11
Page 281 and 282:
252 B.1.2 Partial Coherence Between
Page 283 and 284:
254
Page 285 and 286:
256 Block Diagram !rime of record K
Page 287 and 288:
258
Page 289 and 290:
260 B.2.2 Time — Frequency Analys
Page 291 and 292:
262 This program provides the STFT
Page 293 and 294:
264 G(:j+1)=G(:,j+1)/(2*sum(G(:j+1)
Page 295 and 296:
266 T=(length(Signa)/sample)/(Times
Page 297 and 298:
268 subplot(3, 1,3), plot(T,E); xla
Page 299 and 300:
270 4. The program creates five out
Page 301 and 302:
272 B.2.3.4 Program to Generate Sym
Page 303 and 304:
274 ylabel('frequency'); title('Ins
Page 305 and 306:
276 The program will run and output
Page 307 and 308:
278 axis([0 1 0 2]); grid on; xlabe
Page 309 and 310:
280 vagal=sum(TFDs(HFC,1:k)); symto
Page 311 and 312:
282 plot(J,symtopar); %plot(A,symto
Page 313 and 314:
284 4. Remove the constant levels a
Page 315 and 316:
286 Make sure the agreement is quit
Page 317 and 318:
288 B.2.6 Principal Components Anal
Page 319 and 320:
290 Columns 12 through 15 'LF_pcoh_
Page 321 and 322:
292 I= 1.0000 -0.0000 -0.0000 -0.00
Page 323 and 324:
294 variances = 3.4083 1.2140 1.141
Page 325 and 326:
296 B.2.7 Cluster Analysis Program
Page 327 and 328:
298 end [R,C]=size(Data); if length
Page 329 and 330:
300 B.2.8 Cross-correlation Program
Page 331 and 332:
302 C.3 Partial coherence of HR and
Page 333 and 334:
304 [13] Madwed, J., and R. Cohen.
Page 335 and 336:
306 [41] Mallat, S. G., "A Theory f
Page 337:
[70] Tazebay, M.V., R.T. Saliba and
show all

njit-etd2003-081 - New Jersey Institute of Technology

Create successful ePaper yourself

Delete template?

Save as template?