njit-etd2003-081 - New Jersey Institute of Technology
njit-etd2003-081 - New Jersey Institute of Technology njit-etd2003-081 - New Jersey Institute of Technology
99 3.13.1.3 The Optimal Measurement Configuration. The main goal here is to determine the system transfer function H(ω ) from measurements on the system. The optimal measurement configuration is shown in Figure 3.14. There is no assumption made at this point as to what kind of system is being characterized, biological system or otherwise. This configuration allows the excitation (often called the reference) signal to the system being analyzed, to be measured with negligible error. This is a valid assumption when the output source is measured directly by an input channel as shown in Figure 3.14. Often in biomedical work, the excitation to the system is not in the form of voltage (as is assumed in Figure 3.14). Transducers must be used to convert the system excitation into a voltage which can be measured by the acquisition system. For instance, a force-to-voltage transducer would be used to measure the force in a muscle study. In cases such as this, precautions must be taken to insure that minimal electrical noise corrupts the signal from the electrodes or transducer and that they are operated in their linear region. As shown in Figure 3.14, the entire measurement uncertainty is accounted for in the response signal y,„ (t ) by the additional (unwanted) noise term ny (t) . There are no assumptions about the character of this noise other than when the excitation is zero, the response of the system y (t) is zero, and it is left with ym(t ) = ny (1) . It is important to note that ny (t) is usually not an actual external source but merely a representation of the system output when there is no excitation. At first it might seem that the restriction of having a noiseless reference channel is an unreasonable measurement condition. In practice, however, this requirement is
100 usually attainable. The key point is that an unbiased estimate of the transfer function is relatively easy to obtain if an accurate measurement of the reference channel is made. The transfer function estimation, H(ω), is computed from cross and auto power spectra estimates as shown in (3.92): where Pxy (ω) is the cross power spectrum between the excitation x m (t ) and response ym (t ) and i3„, (ω) is the auto power spectrum of the excitation signal. These spectral estimates (P„,, (ω) , Pxy (ω)) are computed in MatLab or Lab VIEW using the FFT, windowing, and frequency-domain averaging. When more averaging is used, more data is acquired and processed to refine these estimates. As the amount of averaging used in the computations of the cross and auto power spectra are increased, the estimate H(ω) will converge to the actual transfer function H(ω). This is the key property of an unbiased estimator. The amount of averaging required to attain a given accuracy for the transfer function is a function of the noise ny (t): less noise, less averaging. The coherence is an auxiliary computation often made in conjunction with the transfer function estimate. The coherence calculation in (3.93) gives an indication of the portion of the systems output power due to the input excitation.
- Page 77 and 78: 48 3.3 The Analytic Signal and Inst
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- Page 89 and 90: 60 called the cross Wigner distribu
- 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
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- Page 101 and 102: Figure 3.5 The time-frequency plane
- Page 103 and 104: 74 The measure dadb used in the tra
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- Page 107 and 108: 78 Figure 3.6 Figure depicting the
- Page 109 and 110: 80 The final step to obtain the pow
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- Page 115 and 116: Figure 3.12 Power spectrum of BP II
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- 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
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- Page 133 and 134: 104 eXogenous input (ARX) was used
- Page 135 and 136: 106 The baroreflex, an autonomic re
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- Page 139 and 140: 110 The mathematical solution for t
- Page 141 and 142: 112 3.15 Cluster Analysis The term
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- Page 149 and 150: 120 Sneath and Sokal used the abbre
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- 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
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- Page 163 and 164: 134 4.2.3 Power Spectrum Analysis o
- Page 165 and 166: 136 weighted-average value of the c
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100<br />
usually attainable. The key point is that an unbiased estimate <strong>of</strong> the transfer function is<br />
relatively easy to obtain if an accurate measurement <strong>of</strong> the reference channel is made.<br />
The transfer function estimation, H(ω), is computed from cross and auto power<br />
spectra estimates as shown in (3.92):<br />
where Pxy (ω) is the cross power spectrum between the excitation x m (t ) and response<br />
ym (t ) and i3„, (ω) is the auto power spectrum <strong>of</strong> the excitation signal.<br />
These spectral estimates (P„,, (ω) , Pxy (ω)) are computed in MatLab or Lab VIEW<br />
using the FFT, windowing, and frequency-domain averaging. When more averaging is<br />
used, more data is acquired and processed to refine these estimates.<br />
As the amount <strong>of</strong> averaging used in the computations <strong>of</strong> the cross and auto power<br />
spectra are increased, the estimate H(ω) will converge to the actual transfer function<br />
H(ω). This is the key property <strong>of</strong> an unbiased estimator. The amount <strong>of</strong> averaging<br />
required to attain a given accuracy for the transfer function is a function <strong>of</strong> the noise<br />
ny (t): less noise, less averaging.<br />
The coherence is an auxiliary computation <strong>of</strong>ten made in conjunction with the<br />
transfer function estimate. The coherence calculation in (3.93) gives an indication <strong>of</strong> the<br />
portion <strong>of</strong> the systems output power due to the input excitation.
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