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°
3014681: TIME WAVEFORM
1500
1000
500
5
10
15
20
3014681: FIRST DERIVATIVE
25
5
10
15
20
3014681: SECOND DERIVATIVE
25
5
10
10000
5000
0
−5000
5
5
x 10
0
−5
…‘DŠ
15
20
25
3014681: ENTIRE WAVEFORM WITH DETECTED MAXIMA AND MINIMA
140
DATA
MAX
MIN
130
PRESSURE (mm Hg)
120
110
100
90
80
70
60
0
5
10
15
TIME (sec)
20
25
30
n… j?Š
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D;5BTU9<;?9<TUDd
·
3014681: SIMILAR DECAY PULSES, MEAN, DETECTED NOTCH
130
120
PRESSURE (mm Hg)
110
100
90
80
70
20
40
60
80
100
SAMPLE INDEX
…‘DŠ
120
140
160
3014681: MEAN DECAY PULSE: DATA AND FIT
DATA
EXP. FIT
92
90
PRESSURE (mm Hg)
88
86
84
82
80
78
76
74
0.35
0.4
0.45
0.5
0.55
0.6
TIME (SEC)
0.65
0.7
0.75
0.8
n… j?Š
 9GN35.]*+±Ok—˜DZ68DF10*V6˜¬­¯®2²°f³¯®2O+…nDŠh‰59<TU9G4<Df.§B5*2H\DMa},+DMwx*2ILK.0TU1ƒD;5B’T[*2D;5ys,F9Œ6E>^B5*V6E*\H-68*\B~B59GHY>5.]K2689GH
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³
3014681: MEAN DECAY WAVEFORM
150
100
50
0.1
0.2
0.3
0.4
0.5
0.6
3014681: FIRST DERIVATIVE (SMOOTHED)
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.6
3014681: SECOND DERIVATIVE (SMOOTHED)
0.7
0.8
0.1
0.2
0.6
0.7
0.8
200
0
−200
−400
4
2
x 10
1
0
−1
0.3
0.4
TIME (SEC)
…‘DŠ
0.5
3014681: MEAN DECAY WAVEFORM
150
100
50
0.1
0.2
0.3
0.4
0.5
3014681: FIRST DERIVATIVE
0.6
0.7
0.8
0.1
0.2
0.3
0.4
0.5
3014681: SECOND DERIVATIVE
0.6
0.7
0.8
0.1
0.2
0.6
0.7
0.8
200
0
−200
−400
4
2
x 10
1
0
−1
0.3
0.4
TIME (SEC)
0.5
n… j?Š
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10TUKK268>?9<;5Nfd
¸
PRESSURE (mm Hg)
3014681: RMS ERROR OF FIT VERSUS NOTCH LOCATION
1
0.8
0.6
0.4
0.2
20
40
60
80
100
NORMALIZED RMS ERROR ...
120
140
160
20
40
60
80
100
MAX ABSOLUTE ERROR ...
120
140
160
20
40
60
80
100
CANDIDATE NOTCH INDEX
120
140
160
−3
x 10
12
10
8
6
4
PRESSURE (mm Hg)
2
3
2
1
…‘DŠ
3014681: TIME CONSTANT VERSUS TRUNC. OFFSET
0.4
0.35
0.3
0.25
20
40
60
80
100
120
EXPONENTIAL MODEL AMPLITUDE (A)
140
160
20
40
60
80
100
120
EXPONENTIAL MODEL CONSTANT (B)
140
160
20
40
140
160
1000
900
800
700
600
680
660
640
60
80
100
CANDIDATE NOTCH INDEX
120
n… j?Š
 9GN35.]*[²fO}—˜D26EDc1]*V6’¬­¯®2²f°³¯®2O…‘DŠ{zuKKqB?;5*\1]1nmYKfIomYpS6[TU*\Df1035.]*\1|6EKc*-r ACK;5*2;E689GD4T[KB5*24ILKf.FB?9<©C*\.‘m
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®2­
3014681: SIMILAR FULL−CYCLE PULSES AND MEAN
130
120
PRESSURE (mm Hg)
110
100
90
80
70
20
40
60
80
100
120
SAMPLE INDEX
140
160
 9<N3?.0*J¹Oƒ—˜D26ED=10*V6l¬­¯®Z²°³¯®2Oh‰59GT[9G4GD.@IL354<47mYH-avH\4G*uA53?4<1]*\1+Df;5B~T[*2D;5d
®®
180
3014681: MAGNITUDE OF FORWARD TF (INTERPOLATED)
4
3
3
AMPLIFICATION
AMPLIFICATION
MAGNITUDE OF FORWARD TRANSFER FUNCTION
4
2
1
0
2
1
0
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
8
9
10
0
5
10
15
FREQUENCY (Hz)
PHASE OF FORWARD TRANSFER FUNCTION
PHASE OF FORWARD TF (INTERPOLATED)
0
PHASE (RADIANS)
PHASE (RADIANS)
0
−2
−4
−6
−8
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
…nDfŠ
8
9
−2
−4
−6
−8
10
0
5
3014681: MAGNITUDE OF INVERSE TF (INTERPOLATED)
AMPLIFICATION
…nj?Š
10
15
FREQUENCY (Hz)
3014681: FFT MAGNITUDE OF MEAN FULL−CYCLE PULSE
20
105
15
100
10
95
5
90
0
85
0
5
10
15
dB
FREQUENCY (Hz)
80
PHASE OF INVERSE TF (INTERPOLATED)
PHASE (RADIANS)
8
75
6
70
4
65
2
60
0
0
5
10
15
0
5
10
15
FREQUENCY (Hz)
20
25
‘… H\Š
…nB5Š
 9GN35.]*F°fO:—˜DZ68D=10*-6›¬f­¯®2²°³x®2OJ…nDfŠMx1‘689GT[DZ68*FKItILKf.n,+D.0B eƒ yXIL.0KfT A535j?4<9G10>5*2BN.]DA5>5du…nj?ŠMaƒ3?j59<H-m
10A?4<9G;5*‚9G;86E*\.]AvK4GD26E*\B#ILK.‘,ŽD.]B eƒ d=…‘H\~Š aƒ35j59GHVmY1]A54G9<;5*9G;E68*\.]AvKf4<D26E*\B#9G;Ewx*\.]10* eƒ y,F9Œ6E>#–\*\.]KND9G;
jC*VaxKf;5B;59G;E68>>5D.]T[Kf;59<H2du…nB5Š &&e TUDN;597683?B5*JKITU*\Df;cIL354G47mYHVavH24<*FA5354G10*2d
®2±
FREQUENCY (Hz)
30
3014681: FULL−CYCLE PULSE, AFTER INVERSE TRANSFORM
1800
1600
PRESSURE (mm Hg)
1400
1200
1000
800
600
400
200
−2
−1.5
−1
−0.5
0
TIME (SEC)
…‘DŠ
0.5
1
1.5
2
3014681: FULL−CYCLE PULSE, BEFORE & AFTER INVERSE TF
1
0.9
0.8
NORMALIZED PRESSURE
0.7
0.6
0.5
0.4
0.3
ORIGINAL PULSE
AFTER INVERSE TRANSFORM
0.2
0.1
0
−2
−1.5
−1
−0.5
0
TIME (SEC)
0.5
1
1.5
2
n… j?Š
 9GN35.]*Ž·Ok—˜D26ED›10*-6J¬­¯®Z²°³¯®2OŽ…nDŠh‡|*21035476FKIXA5Df10109G;5NUTU*\D;iIL3?4<47mYH-a H24<*˜A?354<1]*§68>5.]K35N>i9G;Ewx*2.010* eƒ d
…nj?Š  354G47mYHVavH24<*JA5354G10*FjC*\ILK.]*FDf;5B~DIo68*2.:9G;Ewx*2.010*@68.]D;510ILKf.0TUyq,F9768>AC*\Df^A5.0*2101]35.0*F;5K.]T[Df4<9G–\*2B[68Kc®2d
®2¬
FORWARD IMPULSE RESPONSE
0.1
0.05
0
−0.05
−0.1
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
1.5
2
IMPULSE RESPONSE OF INVERSE TRANSFER FUNCTION
0.2
0.15
0.1
0.05
0
−2
−1.5
−1
−0.5
0
TIME (sec)
0.5
1
 G9 N35.]*:³fO§—˜D26EDu1]*V6+¬­¯®2²°f³¯®2Oœ«T[A?354<1]*+.]*\10ACK;51]*\1hKI ILK.‘,ŽDf.0B[D;5B’9G;Ewx*2.010* eƒ 10d e >?*+H\Kf;8w5K4G3S689GK;
KI568>?*\10*k6«,+K}9GTUA5354G10*J.0*210ACK;51]*\1:.0*\1]*\Tuj54<*21|Df;9GTUA5354G10*2yzDf1ƒ9Œ6J1]>5K354GB109G;5H\*k68>?*\10*JD.]*˜9<;Ew5*\.01]*\1:KI
*\DfHY>cK26E>5*\.]d
®2²
3011623: TIME WAVEFORM
1200
1000
800
600
5
10
15
20
3011623: FIRST DERIVATIVE
25
5
10
15
20
3011623: SECOND DERIVATIVE
25
5
10
10000
5000
0
−5000
5
5
x 10
0
−5
…‘DŠ
15
20
25
3011623: ENTIRE WAVEFORM WITH DETECTED MAXIMA AND MINIMA
120
DATA
MAX
MIN
110
PRESSURE (mm Hg)
100
90
80
70
60
0
5
10
15
TIME (sec)
20
25
30
n… j?Š
 9GN35.]*’¸O~—˜D26ED10*-6~¬­¯®f®2°±¬OW…‘DŠyx;E689G.0*F,ŽDMwx*2ILK.0T DTUBB5*\.]9ŒwqD26E9Œw5*\1]d؅‘j5Šl—˜*-68*2HV68*2BTUD2rv9<TUD
D;5BTU9<;?9<TUDd
®2¹
3011623: SIMILAR DECAY PULSES, MEAN, DETECTED NOTCH
110
105
100
PRESSURE (mm Hg)
95
90
85
80
75
70
65
20
40
60
80
SAMPLE INDEX
…‘DŠ
100
120
140
3011623: MEAN DECAY PULSE: DATA AND FIT
DATA
EXP. FIT
76
PRESSURE (mm Hg)
74
72
70
68
66
0.4
0.45
0.5
0.55
0.6
TIME (SEC)
0.65
0.7
0.75
n… j?Š
 9GN35.]*J®2­O—˜D26EDŽ10*-6@¬­¯®®Z°±¬O|…nDfŠ‰59GTU9<4GD.&B5*2H\DMal,+DMwx*2ILK.0TU1D;5B=TU*\Df;5yS,F9768>=B5*-68*\H-68*2B}B59GHY>5.]K2689GH
;5K26EHY>c9G;5B59GH\DZ68*\BcjEa^wx*2.n689GH\Df4z4G9G;5*\dl…nj5ŠƒˆK;5K*VrvAvKf;5*\;E689GD4¨pS6uIL.0KfT ;5K26EHY>U6EKUB59<Df1n68Kf4<*2d
®2°
3011623: MEAN DECAY WAVEFORM
120
100
80
60
0.1
0.2
0.1
0.1
0.3
0.4
0.5
3011623: FIRST DERIVATIVE (SMOOTHED)
0.6
0.7
0.2
0.3
0.4
0.5
3011623: SECOND DERIVATIVE (SMOOTHED)
0.6
0.7
0.2
0.6
0.7
0
−100
−200
−300
4
1
x 10
0.5
0
−0.5
−1
0.3
0.4
TIME (SEC)
…‘DŠ
0.5
3011623: MEAN DECAY WAVEFORM
120
100
80
60
0.1
0.2
0.3
0.4
0.5
3011623: FIRST DERIVATIVE
0.6
0.7
0.1
0.2
0.3
0.4
0.5
3011623: SECOND DERIVATIVE
0.6
0.7
0.1
0.2
0.6
0.7
200
0
−200
−400
4
5
x 10
0
−5
0.3
0.4
TIME (SEC)
0.5
n… j?Š
 9GN35.]*˜®®2O—˜D26ED+10*-6@¬­¯®f®2°±¬Oˆ*\D;=B5*2H\DMaF,ŽDMwx*2ILK.0T¦D;5B=B5*2.097wqD26897wx*21:…nDŠ¯,F9Œ6E>=D;5B~…‘j5ŠC,F9768>5Kf3S6
10TUKK268>?9<;5Nfd
®2·
PRESSURE (mm Hg)
3011623: RMS ERROR OF FIT VERSUS NOTCH LOCATION
0.4
0.3
0.2
0.1
20
40
60
80
100
NORMALIZED RMS ERROR ...
120
140
20
40
60
80
100
MAX ABSOLUTE ERROR ...
120
140
20
40
60
80
100
CANDIDATE NOTCH INDEX
120
140
−3
x 10
6
5
4
3
PRESSURE (mm Hg)
2
1.5
1
0.5
…‘DŠ
3011623: TIME CONSTANT VERSUS TRUNC. OFFSET
0.5
0.45
0.4
0.35
0.3
20
40
60
80
100
EXPONENTIAL MODEL AMPLITUDE (A)
120
140
20
40
60
80
100
EXPONENTIAL MODEL CONSTANT (B)
120
140
20
40
120
140
650
600
550
600
580
560
540
60
80
100
CANDIDATE NOTCH INDEX
n… j?Š
 9GN35.]*i®2±O˜—˜DZ68D[10*V6=¬­¯®®2°f±¬OU…‘DŠzFKKqB5;?*\101‘mYKIomMpS6lT[*2D103?.0*\1§6EK’*-r ACK;5*2;E689GD4TUKB5*\4tILK.|B?9<©C*\.‘m
*\;E6’HY>5K9GH\*21lKIB59GHY>5.0K26E9<H[;5K26EHY>†4GKqH2D2689GK;5d“…‘j5}Š |:D.09GD2689GK;W9<;W*VrvACK;5*2;86E9<Df4TUKB5*\4A5Df.0DTU*V6E*\.]1FILKf.
B59G©v*2.0*2;86lHY>5K9GH\*21|KfItB59GHY>5.]K2689GHu;?K268HY>4<KH\DZ689GK;5d
®2³
3011623: SIMILAR FULL−CYCLE PULSES AND MEAN
110
105
100
PRESSURE (mm Hg)
95
90
85
80
75
70
65
20
40
60
80
100
SAMPLE INDEX
120
140
160
 9GN35.]*[®2¬Oƒ—˜D26EDU10*V6u¬­x®®2°±¬fOk‰59GT[9G4GD.@IL354<47mYH-avH\4G*uA53?4<1]*\1:D;5BT[*2D;5d
®2¸
180
3011623: MAGNITUDE OF FORWARD TF (INTERPOLATED)
4
3
3
AMPLIFICATION
AMPLIFICATION
MAGNITUDE OF FORWARD TRANSFER FUNCTION
4
2
1
0
2
1
0
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
8
9
10
0
5
10
15
FREQUENCY (Hz)
PHASE OF FORWARD TRANSFER FUNCTION
PHASE OF FORWARD TF (INTERPOLATED)
0
PHASE (RADIANS)
PHASE (RADIANS)
0
−2
−4
−6
−8
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
…nDfŠ
8
9
−2
−4
−6
−8
10
0
5
…nj?Š
10
15
FREQUENCY (Hz)
3011623: MAGNITUDE OF INVERSE TF (INTERPOLATED)
3011623: FFT MAGNITUDE OF MEAN FULL−CYCLE PULSE
AMPLIFICATION
20
100
15
95
10
90
5
85
0
0
5
10
15
dB
FREQUENCY (Hz)
80
PHASE (RADIANS)
PHASE OF INVERSE TF (INTERPOLATED)
8
75
6
70
4
65
2
60
0
55
0
5
10
15
0
5
10
15
FREQUENCY (Hz)
20
25
‘… H\Š
…nB5Š
 9GN35.]*›®2²fO§—˜D26EDu1]*V6˜¬f­¯®®2°±f¬OŽ…‘DŠ€x1n689GTUD268*+KI ILK.‘,ŽDf.0B eƒ yCIL.]KTgA535j?4<9G10>5*2BiN.0DfA5>5dJ…‘j5Šaƒ3?j59<H-m
10A?4<9G;5*‚9G;86E*\.]AvK4GD26E*\B#ILK.‘,ŽD.]B eƒ d=…‘H\~Š aƒ35j59GHVmY1]A54G9<;5*9G;E68*\.]AvKf4<D26E*\B#9G;Ewx*\.]10* eƒ y,F9Œ6E>#–\*\.]KND9G;
jC*VaxKf;5B;59G;E68>>5D.]T[Kf;59<H2du…nB5Š &&e TUDN;597683?B5*JKITU*\Df;cIL354G47mYHVavH24<*FA5354G10*2d
±­
FREQUENCY (Hz)
30
3011623: FULL−CYCLE PULSE, AFTER INVERSE TRANSFORM
1600
1400
PRESSURE (mm Hg)
1200
1000
800
600
400
200
−2
−1.5
−1
−0.5
0
TIME (SEC)
…‘DŠ
0.5
1
1.5
2
3011623: FULL−CYCLE PULSE, BEFORE & AFTER INVERSE TF
1
ORIGINAL PULSE
AFTER INVERSE TRANSFORM
0.9
0.8
NORMALIZED PRESSURE
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−2
−1.5
−1
−0.5
0
TIME (SEC)
0.5
1
1.5
2
n… j?Š
 9GN35.]*F®2¹O—˜D268D˜1]*V6|¬­¯®®Z°±¬O|…nDfŠ&‡|*21035476|KICA5D101]9<;?NFTU*2D;}IL3?4<47mYH-a H24<*@A53?4<1]*6E>5.0Kf35N>U9<;Ew5*\.01]* eƒ d
…nj?Š  354G47mYHVavH24<*JA5354G10*FjC*\ILK.]*FDf;5B~DIo68*2.:9G;Ewx*2.010*@68.]D;510ILKf.0TUyq,F9768>AC*\Df^A5.0*2101]35.0*F;5K.]T[Df4<9G–\*2B[68Kc®2d
±¯®
7010150: TIME WAVEFORM
1500
1000
500
5
10
15
20
7010150: FIRST DERIVATIVE
25
5
10
15
20
7010150: SECOND DERIVATIVE
25
5
10
10000
5000
0
−5000
5
5
x 10
0
−5
…‘DŠ
15
20
25
7010150: ENTIRE WAVEFORM WITH DETECTED MAXIMA AND MINIMA
130
DATA
MAX
MIN
120
PRESSURE (mm Hg)
110
100
90
80
70
0
5
10
15
TIME (sec)
20
25
30
n… j?Š
 9GN35.]*®2°O=—˜D26EDi10*V6}·­x®2­¯®2¹­fOi…nDfŠ‚x;E6E9<.]*J,+DMwx*\ILKf.0TÍDTUBB5*\.]9ŒwqD26E9Œw5*\1]d”…‘j5Š˜—˜*V6E*\HV6E*\BWTUD2rv9<TUD
D;5BTU9<;?9<TUDd
±±
7010150: SIMILAR DECAY PULSES, MEAN, DETECTED NOTCH
120
115
PRESSURE (mm Hg)
110
105
100
95
90
85
20
40
60
80
100
SAMPLE INDEX
…‘DŠ
120
140
160
180
7010150: MEAN DECAY PULSE: DATA AND FIT
DATA
EXP. FIT
90
89
PRESSURE (mm Hg)
88
87
86
85
84
83
0.55
0.6
0.65
0.7
0.75
TIME (SEC)
0.8
0.85
0.9
n… j?Š
 9GN35.]*J®2·O—˜D26EDŽ10*-6@·­¯®2­x®2¹­O|…nDfŠ‰59GTU9<4GD.&B5*2H\DMal,+DMwx*2ILK.0TU1D;5B=TU*\Df;5yS,F9768>=B5*-68*\H-68*2B}B59GHY>5.]K2689GH
;5K26EHY>c9G;5B59GH\DZ68*\BcjEa^wx*2.n689GH\Df4z4G9G;5*\dl…nj5ŠƒˆK;5K*VrvAvKf;5*\;E689GD4¨pS6uIL.0KfT ;5K26EHY>U6EKUB59<Df1n68Kf4<*2d
±¬
7010150: MEAN DECAY WAVEFORM
120
110
100
90
80
0.1
0.2
0.3
0.4
0.5
0.6
7010150: FIRST DERIVATIVE (SMOOTHED)
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.6
7010150: SECOND DERIVATIVE (SMOOTHED)
0.7
0.8
0.1
0.2
0.7
0.8
200
0
−200
−400
4
2
x 10
1
0
−1
0.3
0.4
0.5
TIME (SEC)
…‘DŠ
0.6
7010150: MEAN DECAY WAVEFORM
120
110
100
90
80
0.1
0.2
0.3
0.4
0.5
0.6
7010150: FIRST DERIVATIVE
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.6
7010150: SECOND DERIVATIVE
0.7
0.8
0.1
0.2
0.3
0.7
0.8
200
0
−200
−400
4
5
x 10
0
−5
0.4
0.5
TIME (SEC)
0.6
n… j?Š
 9GN35.]*˜®2³O—˜D26ED+10*-6@·­¯®Z­¯®2¹­Oˆ*\D;=B5*2H\DMaF,ŽDMwx*2ILK.0T¦D;5B=B5*2.097wqD26897wx*21:…nDŠ¯,F9Œ6E>=D;5B~…‘j5ŠC,F9768>5Kf3S6
10TUKK268>?9<;5Nfd
±²
PRESSURE (mm Hg)
7010150: RMS ERROR OF FIT VERSUS NOTCH LOCATION
1
0.8
0.6
0.4
0.2
20
40
60
80
100
120
NORMALIZED RMS ERROR ...
140
160
180
20
40
60
80
100
120
MAX ABSOLUTE ERROR ...
140
160
180
20
40
60
80
100
120
CANDIDATE NOTCH INDEX
140
160
180
−3
x 10
10
8
6
4
PRESSURE (mm Hg)
2
3
2
1
…‘DŠ
7010150: TIME CONSTANT VERSUS TRUNC. OFFSET
0.6
0.5
0.4
0.3
20
40
60
80
100
120
EXPONENTIAL MODEL AMPLITUDE (A)
140
160
180
20
40
60
80
100
120
EXPONENTIAL MODEL CONSTANT (B)
140
160
180
20
40
140
160
180
900
800
700
600
500
800
750
700
60
80
100
120
CANDIDATE NOTCH INDEX
n… j?Š
 9GN35.]*i®2¸O˜—˜DZ68D[10*V6=·­¯®2­¯®Z¹­OU…‘DŠzFKKqB5;?*\101‘mYKIomMpS6lT[*2D103?.0*\1§6EK’*-r ACK;5*2;E689GD4TUKB5*\4tILK.|B?9<©C*\.‘m
*\;E6’HY>5K9GH\*21lKIB59GHY>5.0K26E9<H[;5K26EHY>†4GKqH2D2689GK;5d“…‘j5}Š |:D.09GD2689GK;W9<;W*VrvACK;5*2;86E9<Df4TUKB5*\4A5Df.0DTU*V6E*\.]1FILKf.
B59G©v*2.0*2;86lHY>5K9GH\*21|KfItB59GHY>5.]K2689GHu;?K268HY>4<KH\DZ689GK;5d
±¹
7010150: SIMILAR FULL−CYCLE PULSES AND MEAN
120
115
PRESSURE (mm Hg)
110
105
100
95
90
85
80
20
40
60
80
100
120
SAMPLE INDEX
140
160
 9GN35.]*˜±­Oƒ—˜D26EDU10*V6u·­x®2­¯®2¹­fOk‰59GT[9G4GD.@IL354<47mYH-avH\4G*uA53?4<1]*\1:D;5BT[*2D;5d
±°
180
200
7010150: MAGNITUDE OF FORWARD TF (INTERPOLATED)
4
3
3
AMPLIFICATION
AMPLIFICATION
MAGNITUDE OF FORWARD TRANSFER FUNCTION
4
2
1
0
2
1
0
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
8
9
10
0
5
10
15
FREQUENCY (Hz)
PHASE OF FORWARD TRANSFER FUNCTION
PHASE OF FORWARD TF (INTERPOLATED)
0
PHASE (RADIANS)
PHASE (RADIANS)
0
−2
−4
−6
−8
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
…nDfŠ
8
9
−2
−4
−6
−8
10
0
5
7010150: MAGNITUDE OF INVERSE TF (INTERPOLATED)
15
7010150: FFT MAGNITUDE OF MEAN FULL−CYCLE PULSE
20
AMPLIFICATION
…nj?Š
10
FREQUENCY (Hz)
105
15
100
10
95
5
90
0
0
5
10
85
15
dB
FREQUENCY (Hz)
PHASE OF INVERSE TF (INTERPOLATED)
80
8
PHASE (RADIANS)
75
6
70
4
65
2
60
0
0
5
10
15
0
5
10
15
FREQUENCY (Hz)
20
25
‘… H\Š
…nB5Š
 9GN35.]*|±¯®ZO§—˜D26EDu1]*V6˜·f­¯®2­¯®2¹f­OŽ…‘DŠ€x1n689GTUD268*+KI ILK.‘,ŽDf.0B eƒ yCIL.]KTgA535j?4<9G10>5*2BiN.0DfA5>5dJ…‘j5Šaƒ3?j59<H-m
10A?4<9G;5*‚9G;86E*\.]AvK4GD26E*\B#ILK.‘,ŽD.]B eƒ d=…‘H\~Š aƒ35j59GHVmY1]A54G9<;5*9G;E68*\.]AvKf4<D26E*\B#9G;Ewx*\.]10* eƒ y,F9Œ6E>#–\*\.]KND9G;
jC*VaxKf;5B;59G;E68>>5D.]T[Kf;59<H2du…nB5Š &&e TUDN;597683?B5*JKITU*\Df;cIL354G47mYHVavH24<*FA5354G10*2d
±·
FREQUENCY (Hz)
30
7010150: FULL−CYCLE PULSE, AFTER INVERSE TRANSFORM
1800
1600
PRESSURE (mm Hg)
1400
1200
1000
800
600
400
200
−2
−1.5
−1
−0.5
0
TIME (SEC)
…‘DŠ
0.5
1
1.5
2
7010150: FULL−CYCLE PULSE, BEFORE & AFTER INVERSE TF
1
ORIGINAL PULSE
AFTER INVERSE TRANSFORM
0.9
0.8
NORMALIZED PRESSURE
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−2
−1.5
−1
−0.5
0
TIME (SEC)
0.5
1
1.5
2
n… j?Š
 9GN35.]*ƒ±±O—˜D268D˜1]*V6|·­¯®2­x®2¹­O|…nDfŠ&‡|*21035476|KICA5D101]9<;?NFTU*2D;}IL3?4<47mYH-a H24<*@A53?4<1]*6E>5.0Kf35N>U9<;Ew5*\.01]* eƒ d
…nj?Š  354G47mYHVavH24<*JA5354G10*FjC*\ILK.]*FDf;5B~DIo68*2.:9G;Ewx*2.010*@68.]D;510ILKf.0TUyq,F9768>AC*\Df^A5.0*2101]35.0*F;5K.]T[Df4<9G–\*2B[68Kc®2d
±³
7010966: TIME WAVEFORM
1500
1000
500
0
5
10
15
20
7010966: FIRST DERIVATIVE
25
5
10
15
20
7010966: SECOND DERIVATIVE
25
5
10
4
2
x 10
1
0
−1
6
1
x 10
0.5
0
−0.5
−1
…‘DŠ
15
20
25
7010966: ENTIRE WAVEFORM WITH DETECTED MAXIMA AND MINIMA
110
DATA
MAX
MIN
100
PRESSURE (mm Hg)
90
80
70
60
50
40
0
5
10
15
TIME (sec)
20
25
30
n… j?Š
 9GN35.]*=±¬O=—˜D26EDi10*V6}·­x®2­¸°°fOi…nDfŠ‚x;E6E9<.]*J,+DMwx*\ILKf.0TÍDTUBB5*\.]9ŒwqD26E9Œw5*\1]d”…‘j5Š˜—˜*V6E*\HV6E*\BWTUD2rv9<TUD
D;5BTU9<;?9<TUDd
±¸
7010966: SIMILAR DECAY PULSES, MEAN, DETECTED NOTCH
100
95
PRESSURE (mm Hg)
90
85
80
75
70
65
60
55
20
40
60
80
SAMPLE INDEX
…‘DŠ
100
120
140
7010966: MEAN DECAY PULSE: DATA AND FIT
80
DATA
EXP. FIT
PRESSURE (mm Hg)
75
70
65
60
0.3
0.35
0.4
0.45
0.5
0.55
TIME (SEC)
0.6
0.65
0.7
0.75
n… j?Š
 9GN35.]*k±²O—˜D26EDŽ10*-6@·­¯®2­f¸°°O|…nDfŠ‰59GTU9<4GD.&B5*2H\DMal,+DMwx*2ILK.0TU1D;5B=TU*\Df;5yS,F9768>=B5*-68*\H-68*2B}B59GHY>5.]K2689GH
;5K26EHY>c9G;5B59GH\DZ68*\BcjEa^wx*2.n689GH\Df4z4G9G;5*\dl…nj5ŠƒˆK;5K*VrvAvKf;5*\;E689GD4¨pS6uIL.0KfT ;5K26EHY>U6EKUB59<Df1n68Kf4<*2d
¬­
7010966: MEAN DECAY WAVEFORM
100
80
60
40
0.1
0.2
0.1
0.1
0.3
0.4
0.5
7010966: FIRST DERIVATIVE (SMOOTHED)
0.6
0.7
0.2
0.3
0.4
0.5
7010966: SECOND DERIVATIVE (SMOOTHED)
0.6
0.7
0.2
0.6
0.7
200
0
−200
−400
4
2
x 10
1
0
−1
−2
0.3
0.4
TIME (SEC)
…‘DŠ
0.5
7010966: MEAN DECAY WAVEFORM
100
80
60
40
0.1
0.2
0.3
0.4
0.5
7010966: FIRST DERIVATIVE
0.6
0.7
0.1
0.2
0.3
0.4
0.5
7010966: SECOND DERIVATIVE
0.6
0.7
0.1
0.2
0.6
0.7
200
0
−200
−400
4
5
x 10
0
−5
0.3
0.4
TIME (SEC)
0.5
n… j?Š
 9GN35.]*§±¹O—˜D26ED+10*-6@·­¯®Z­¸°°Oˆ*\D;=B5*2H\DMaF,ŽDMwx*2ILK.0T¦D;5B=B5*2.097wqD26897wx*21:…nDŠ¯,F9Œ6E>=D;5B~…‘j5ŠC,F9768>5Kf3S6
10TUKK268>?9<;5Nfd
¬¯®
PRESSURE (mm Hg)
7010966: RMS ERROR OF FIT VERSUS NOTCH LOCATION
0.8
0.6
0.4
20
40
60
80
100
NORMALIZED RMS ERROR ...
120
140
20
40
60
80
100
MAX ABSOLUTE ERROR ...
120
140
20
40
60
80
100
CANDIDATE NOTCH INDEX
120
140
−3
x 10
12
10
8
PRESSURE (mm Hg)
6
3
2
1
…‘DŠ
7010966: TIME CONSTANT VERSUS TRUNC. OFFSET
0.8
0.6
0.4
20
40
60
80
100
EXPONENTIAL MODEL AMPLITUDE (A)
120
140
20
40
60
80
100
EXPONENTIAL MODEL CONSTANT (B)
120
140
20
40
120
140
750
700
650
450
400
350
300
250
60
80
100
CANDIDATE NOTCH INDEX
n… j?Š
 9GN35.]*l±°O˜—˜DZ68D[10*V6=·­¯®2­¸f°°OU…‘DŠzFKKqB5;?*\101‘mYKIomMpS6lT[*2D103?.0*\1§6EK’*-r ACK;5*2;E689GD4TUKB5*\4tILK.|B?9<©C*\.‘m
*\;E6’HY>5K9GH\*21lKIB59GHY>5.0K26E9<H[;5K26EHY>†4GKqH2D2689GK;5d“…‘j5}Š |:D.09GD2689GK;W9<;W*VrvACK;5*2;86E9<Df4TUKB5*\4A5Df.0DTU*V6E*\.]1FILKf.
B59G©v*2.0*2;86lHY>5K9GH\*21|KfItB59GHY>5.]K2689GHu;?K268HY>4<KH\DZ689GK;5d
±
7010966: SIMILAR FULL−CYCLE PULSES AND MEAN
100
95
90
PRESSURE (mm Hg)
85
80
75
70
65
60
55
50
20
40
60
80
100
SAMPLE INDEX
120
140
160
 9GN35.]*˜±·Oƒ—˜D26EDU10*V6u·­x®2­¸°°fOk‰59GT[9G4GD.@IL354<47mYH-avH\4G*uA53?4<1]*\1:D;5BT[*2D;5d
¬¬
180
7010966: MAGNITUDE OF FORWARD TF (INTERPOLATED)
4
3
3
AMPLIFICATION
AMPLIFICATION
MAGNITUDE OF FORWARD TRANSFER FUNCTION
4
2
1
0
2
1
0
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
8
9
10
0
5
10
15
FREQUENCY (Hz)
PHASE OF FORWARD TRANSFER FUNCTION
PHASE OF FORWARD TF (INTERPOLATED)
0
PHASE (RADIANS)
PHASE (RADIANS)
0
−2
−4
−6
−8
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
…nDfŠ
8
9
−2
−4
−6
−8
10
0
5
…nj?Š
10
15
FREQUENCY (Hz)
7010966: MAGNITUDE OF INVERSE TF (INTERPOLATED)
7010966: FFT MAGNITUDE OF MEAN FULL−CYCLE PULSE
20
AMPLIFICATION
100
15
95
10
90
5
85
0
0
5
10
15
PHASE OF INVERSE TF (INTERPOLATED)
PHASE (RADIANS)
80
dB
FREQUENCY (Hz)
8
75
6
70
4
65
2
60
0
55
0
5
10
15
0
5
10
15
FREQUENCY (Hz)
20
25
‘… H\Š
…nB5Š
 9GN35.]*|±³fO§—˜D26EDu1]*V6˜·f­¯®2­¸°f°OŽ…‘DŠ€x1n689GTUD268*+KI ILK.‘,ŽDf.0B eƒ yCIL.]KTgA535j?4<9G10>5*2BiN.0DfA5>5dJ…‘j5Šaƒ3?j59<H-m
10A?4<9G;5*‚9G;86E*\.]AvK4GD26E*\B#ILK.‘,ŽD.]B eƒ d=…‘H\~Š aƒ35j59GHVmY1]A54G9<;5*9G;E68*\.]AvKf4<D26E*\B#9G;Ewx*\.]10* eƒ y,F9Œ6E>#–\*\.]KND9G;
jC*VaxKf;5B;59G;E68>>5D.]T[Kf;59<H2du…nB5Š &&e TUDN;597683?B5*JKITU*\Df;cIL354G47mYHVavH24<*FA5354G10*2d
¬²
FREQUENCY (Hz)
30
7010966: FULL−CYCLE PULSE, AFTER INVERSE TRANSFORM
1400
PRESSURE (mm Hg)
1200
1000
800
600
400
200
−2
−1.5
−1
−0.5
0
TIME (SEC)
…‘DŠ
0.5
1
1.5
2
7010966: FULL−CYCLE PULSE, BEFORE & AFTER INVERSE TF
1
ORIGINAL PULSE
AFTER INVERSE TRANSFORM
0.9
0.8
NORMALIZED PRESSURE
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−2
−1.5
−1
−0.5
0
TIME (SEC)
0.5
1
1.5
2
n… j?Š
 9GN35.]*ƒ±¸O—˜D268D˜1]*V6|·­¯®2­f¸°°O|…nDfŠ&‡|*21035476|KICA5D101]9<;?NFTU*2D;}IL3?4<47mYH-a H24<*@A53?4<1]*6E>5.0Kf35N>U9<;Ew5*\.01]* eƒ d
…nj?Š  354G47mYHVavH24<*JA5354G10*FjC*\ILK.]*FDf;5B~DIo68*2.:9G;Ewx*2.010*@68.]D;510ILKf.0TUyq,F9768>AC*\Df^A5.0*2101]35.0*F;5K.]T[Df4<9G–\*2B[68Kc®2d
¬¹
7016670: TIME WAVEFORM
1500
1000
500
5
10
15
20
7016670: FIRST DERIVATIVE
25
5
10
15
20
7016670: SECOND DERIVATIVE
25
5
10
4
2
x 10
1
0
−1
6
1
x 10
0.5
0
−0.5
−1
…‘DŠ
15
20
25
7016670: ENTIRE WAVEFORM WITH DETECTED MAXIMA AND MINIMA
140
DATA
MAX
MIN
130
PRESSURE (mm Hg)
120
110
100
90
80
70
60
0
5
10
15
TIME (sec)
20
25
30
n… j?Š
 9GN35.]*=¬­O=—˜D26EDi10*V6}·­x®2°°·­fOi…nDfŠ‚x;E6E9<.]*J,+DMwx*\ILKf.0TÍDTUBB5*\.]9ŒwqD26E9Œw5*\1]d”…‘j5Š˜—˜*V6E*\HV6E*\BWTUD2rv9<TUD
D;5BTU9<;?9<TUDd
¬°
7016670: SIMILAR DECAY PULSES, MEAN, DETECTED NOTCH
130
PRESSURE (mm Hg)
120
110
100
90
80
70
20
40
60
80
100
SAMPLE INDEX
120
…‘DŠ
140
160
7016670: MEAN DECAY PULSE: DATA AND FIT
DATA
EXP. FIT
100
PRESSURE (mm Hg)
95
90
85
80
75
0.4
0.45
0.5
0.55
0.6
0.65
TIME (SEC)
0.7
0.75
0.8
0.85
n… j?Š
 9GN35.]*k¬¯®2O—˜D26EDŽ10*-6@·­¯®2°f°·­O|…nDfŠ‰59GTU9<4GD.&B5*2H\DMal,+DMwx*2ILK.0TU1D;5B=TU*\Df;5yS,F9768>=B5*-68*\H-68*2B}B59GHY>5.]K2689GH
;5K26EHY>c9G;5B59GH\DZ68*\BcjEa^wx*2.n689GH\Df4z4G9G;5*\dl…nj5ŠƒˆK;5K*VrvAvKf;5*\;E689GD4¨pS6uIL.0KfT ;5K26EHY>U6EKUB59<Df1n68Kf4<*2d
¬·
7016670: MEAN DECAY WAVEFORM
150
100
50
0.1
0.2
0.3
0.4
0.5
0.6
7016670: FIRST DERIVATIVE (SMOOTHED)
0.7
0.8
0.1
0.2
0.3
0.4
0.5
0.6
7016670: SECOND DERIVATIVE (SMOOTHED)
0.7
0.8
0.1
0.2
0.7
0.8
200
0
−200
−400
10000
5000
0
−5000
0.3
0.4
0.5
TIME (SEC)
…‘DŠ
0.6
7016670: MEAN DECAY WAVEFORM
150
100
50
0.1
0.2
0.3
0.4
0.5
7016670: FIRST DERIVATIVE
0.6
0.7
0.8
0.1
0.2
0.3
0.4
0.5
7016670: SECOND DERIVATIVE
0.6
0.7
0.8
0.1
0.2
0.3
0.6
0.7
0.8
200
0
−200
−400
4
5
x 10
0
−5
0.4
0.5
TIME (SEC)
n… j?Š
 9GN35.]*§¬±O—˜D26ED+10*-6@·­¯®Z°°·­Oˆ*\D;=B5*2H\DMaF,ŽDMwx*2ILK.0T¦D;5B=B5*2.097wqD26897wx*21:…nDŠ¯,F9Œ6E>=D;5B~…‘j5ŠC,F9768>5Kf3S6
10TUKK268>?9<;5Nfd
¬³
PRESSURE (mm Hg)
7016670: RMS ERROR OF FIT VERSUS NOTCH LOCATION
1
0.8
0.6
0.4
0.2
20
40
60
80
100
120
NORMALIZED RMS ERROR ...
140
160
20
40
60
80
100
MAX ABSOLUTE ERROR ...
120
140
160
20
40
60
80
100
CANDIDATE NOTCH INDEX
120
140
160
−3
12
x 10
10
8
6
PRESSURE (mm Hg)
4
2.5
2
1.5
1
0.5
…‘DŠ
7016670: TIME CONSTANT VERSUS TRUNC. OFFSET
0.7
0.6
0.5
0.4
20
40
60
80
100
120
EXPONENTIAL MODEL AMPLITUDE (A)
140
160
20
40
60
80
100
120
EXPONENTIAL MODEL CONSTANT (B)
140
160
20
40
140
160
1300
1200
1100
600
550
500
450
400
60
80
100
CANDIDATE NOTCH INDEX
120
n… j?Š
 9GN35.]*l¬¬O˜—˜DZ68D[10*V6=·­¯®2°°f·­OU…‘DŠzFKKqB5;?*\101‘mYKIomMpS6lT[*2D103?.0*\1§6EK’*-r ACK;5*2;E689GD4TUKB5*\4tILK.|B?9<©C*\.‘m
*\;E6’HY>5K9GH\*21lKIB59GHY>5.0K26E9<H[;5K26EHY>†4GKqH2D2689GK;5d“…‘j5}Š |:D.09GD2689GK;W9<;W*VrvACK;5*2;86E9<Df4TUKB5*\4A5Df.0DTU*V6E*\.]1FILKf.
B59G©v*2.0*2;86lHY>5K9GH\*21|KfItB59GHY>5.]K2689GHu;?K268HY>4<KH\DZ689GK;5d
¬¸
7016670: SIMILAR FULL−CYCLE PULSES AND MEAN
130
PRESSURE (mm Hg)
120
110
100
90
80
70
20
40
60
80
100
120
SAMPLE INDEX
140
160
 9GN35.]*˜¬²Oƒ—˜D26EDU10*V6u·­x®2°°·­fOk‰59GT[9G4GD.@IL354<47mYH-avH\4G*uA53?4<1]*\1:D;5BT[*2D;5d
²­
180
7016670: MAGNITUDE OF FORWARD TF (INTERPOLATED)
4
3
3
AMPLIFICATION
AMPLIFICATION
MAGNITUDE OF FORWARD TRANSFER FUNCTION
4
2
1
0
2
1
0
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
8
9
10
0
5
10
15
FREQUENCY (Hz)
PHASE OF FORWARD TRANSFER FUNCTION
PHASE OF FORWARD TF (INTERPOLATED)
0
PHASE (RADIANS)
PHASE (RADIANS)
0
−2
−4
−6
−8
0
1
2
3
4
5
6
7
FREQUENCY (NORMALIZED BY HEART RATE)
…nDfŠ
8
9
−2
−4
−6
−8
10
0
5
7016670: MAGNITUDE OF INVERSE TF (INTERPOLATED)
15
7016670: FFT MAGNITUDE OF MEAN FULL−CYCLE PULSE
20
AMPLIFICATION
…nj?Š
10
FREQUENCY (Hz)
105
15
100
10
95
5
90
0
0
5
10
85
15
dB
FREQUENCY (Hz)
PHASE OF INVERSE TF (INTERPOLATED)
80
8
PHASE (RADIANS)
75
6
70
4
65
2
60
0
0
5
10
15
0
5
10
15
FREQUENCY (Hz)
20
25
‘… H\Š
…nB5Š
 9GN35.]*|¬¹fO§—˜D26EDu1]*V6˜·f­¯®2°°·f­OŽ…‘DŠ€x1n689GTUD268*+KI ILK.‘,ŽDf.0B eƒ yCIL.]KTgA535j?4<9G10>5*2BiN.0DfA5>5dJ…‘j5Šaƒ3?j59<H-m
10A?4<9G;5*‚9G;86E*\.]AvK4GD26E*\B#ILK.‘,ŽD.]B eƒ d=…‘H\~Š aƒ35j59GHVmY1]A54G9<;5*9G;E68*\.]AvKf4<D26E*\B#9G;Ewx*\.]10* eƒ y,F9Œ6E>#–\*\.]KND9G;
jC*VaxKf;5B;59G;E68>>5D.]T[Kf;59<H2du…nB5Š &&e TUDN;597683?B5*JKITU*\Df;cIL354G47mYHVavH24<*FA5354G10*2d
²¯®
FREQUENCY (Hz)
30
7016670: FULL−CYCLE PULSE, AFTER INVERSE TRANSFORM
2000
1800
PRESSURE (mm Hg)
1600
1400
1200
1000
800
600
400
200
−2
−1.5
−1
−0.5
0
TIME (SEC)
…‘DŠ
0.5
1
1.5
2
7016670: FULL−CYCLE PULSE, BEFORE & AFTER INVERSE TF
1
ORIGINAL PULSE
AFTER INVERSE TRANSFORM
0.9
0.8
NORMALIZED PRESSURE
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−2
−1.5
−1
−0.5
0
TIME (SEC)
0.5
1
1.5
2
n… j?Š
 9GN35.]*ƒ¬°O—˜D268D˜1]*V6|·­¯®2°f°·­O|…nDfŠ&‡|*21035476|KICA5D101]9<;?NFTU*2D;}IL3?4<47mYH-a H24<*@A53?4<1]*6E>5.0Kf35N>U9<;Ew5*\.01]* eƒ d
…nj?Š  354G47mYHVavH24<*JA5354G10*FjC*\ILK.]*FDf;5B~DIo68*2.:9G;Ewx*2.010*@68.]D;510ILKf.0TUyq,F9768>AC*\Df^A5.0*2101]35.0*F;5K.]T[Df4<9G–\*2B[68Kc®2d
²±