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Introduction to Systems Analysis and Numerical Methods |
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1 | (10) |
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The Systems Approach to Physiological Analysis |
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1 | (2) |
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Physiological Signals and Systems |
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2 | (1) |
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Linear Systems Modeling in Physiology |
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3 | (1) |
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Numerical Methods for Data Analysis and Simulation |
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3 | (5) |
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Numerical Integration and Differentiation |
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4 | (3) |
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7 | (1) |
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Examples of Physiological Models |
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8 | (3) |
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9 | (2) |
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Continous Time Signals and Systems |
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11 | (20) |
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Physiological Measurement and Analysis |
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11 | (1) |
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12 | (4) |
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Examples of Physiological Signals |
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12 | (1) |
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Operations on Time Signals |
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13 | (3) |
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16 | (15) |
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16 | (2) |
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Linear Time-Invariant Systems |
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18 | (2) |
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Impulse Response of a Linear Time-Invariant System |
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20 | (1) |
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21 | (1) |
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Properties of Convolution |
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22 | (8) |
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30 | (1) |
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Fourier Analysis for Continuous Time Processes |
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31 | (36) |
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Decomposition of Periodic Signals |
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31 | (5) |
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Synthesis of an ECG Signal Using Pure Sinusoids |
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32 | (4) |
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36 | (10) |
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Periodic Continuous Time Signals: Fourier Series |
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36 | (6) |
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Aperiodic Continuous Time Signals: Fourier Transform |
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42 | (2) |
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Properties of the Fourier Domain |
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44 | (2) |
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46 | (18) |
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47 | (1) |
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Properties of the Laplace Transform |
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47 | (5) |
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Frequency Response of LTI Systems |
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52 | (1) |
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Pole-Zero Plots and Bode Plots |
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53 | (9) |
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62 | (2) |
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Phase Shifts and Time Delays |
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64 | (1) |
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Systems Representation of Physiological Processes |
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64 | (3) |
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65 | (2) |
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Discrete Time Signals and Systems |
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67 | (34) |
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Discretization of Continuous-Time Signals |
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67 | (10) |
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Sampling and Quantization |
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68 | (1) |
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69 | (4) |
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Reconstruction of a Signal from Its Sampled Version |
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73 | (1) |
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Quantization of Sampled Data |
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74 | (1) |
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Data Conversion Time-Sample and Hold |
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75 | (2) |
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77 | (1) |
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Analogue to Digital Conversion |
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77 | (1) |
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Operations on Discrete-Time Signals |
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77 | (1) |
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78 | (9) |
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The Impulse Response of a Discrete LTI System |
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79 | (1) |
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79 | (1) |
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Properties of the Discrete Convolution Operation |
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80 | (1) |
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Examples of the Convolution Sum |
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80 | (1) |
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Frequency Filtering by Discrete-Time Systems |
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81 | (5) |
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Determination of Impulse Response from I/O Relation |
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86 | (1) |
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87 | (14) |
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Statistical Descriptions of Random Signals |
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91 | (1) |
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Ensemble Average and Time Average |
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92 | (2) |
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94 | (1) |
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Auto-correlation and Cross-Correlation of Discrete Signals |
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95 | (2) |
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97 | (1) |
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98 | (3) |
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Fourier Analysis for Discrete-Time Processes |
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101 | (38) |
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Discrete Fourier Conversions |
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101 | (11) |
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Periodic Discrete Time Signals: Discrete Fourier Series |
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101 | (1) |
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Aperiodic Discrete-Time Signals: DTFT |
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102 | (4) |
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Numerical Implementation of Fourier Conversion: DFT |
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106 | (3) |
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Inter-Relations among Fourier Conversions |
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109 | (3) |
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Applying the Discrete Fourier Transform |
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112 | (10) |
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112 | (3) |
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115 | (2) |
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The Fast Fourier Transform |
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117 | (3) |
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Convolution Using the FFT-Circular Convolution |
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120 | (2) |
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122 | (5) |
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Properties of the Z-transform |
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122 | (3) |
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The Bilinear Transformation |
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125 | (2) |
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Discrete Fourier Transform of Random Signals |
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127 | (12) |
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Estimating the Power Spectrum |
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127 | (2) |
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Transfer Function Estimation or System Identification |
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129 | (1) |
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130 | (2) |
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132 | (7) |
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Time-Frequency and Wavelet Analysis |
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139 | (26) |
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139 | (1) |
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The Short Time Fourier Transform |
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140 | (3) |
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The Continuous Time STFT and the Gabor Transform |
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142 | (1) |
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Wavelet Decomposition of Signals |
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143 | (9) |
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Multi-Resolution Decomposition |
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144 | (1) |
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Hierarchical Filter Bank for Wavelet Decomposition |
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145 | (2) |
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The Daubechies 4-Coefficient Wavelet Filters |
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147 | (5) |
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152 | (9) |
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Interpretation of the Wavelet Transform |
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157 | (1) |
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The Inverse Wavelet Transform |
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158 | (3) |
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Comparison of Fourier and Wavelet Transforms |
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161 | (4) |
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164 | (1) |
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Estimation of Signals in Noise |
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165 | (16) |
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Noise Reduction by Filtering |
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165 | (7) |
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Mean Square Error Minimization |
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166 | (3) |
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169 | (3) |
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172 | (9) |
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Systems with Unknown Inputs-Autoregressive Model |
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173 | (1) |
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Time-Series Model Estimation |
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174 | (3) |
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Recursive Identification of a Non-Stationary Model |
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177 | (2) |
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Time-Series Modeling and Estimation in Physiology |
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179 | (1) |
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179 | (2) |
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181 | (16) |
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Physiological Systems with Feedback |
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181 | (2) |
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Analysis of Feedback Systems |
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183 | (10) |
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Advantages of Feedback Control |
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184 | (5) |
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Analysis of Closed-Loop System Stability using Bode Plots |
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189 | (4) |
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Digital Control in Feedback Systems |
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193 | (4) |
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195 | (2) |
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Model Based Analysis of Physiological Signals |
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197 | (12) |
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Modeling Physiological Systems |
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197 | (3) |
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Biophysical Models and Black Box Models |
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197 | (1) |
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Purpose of Physiological Modeling and Signal Analysis |
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198 | (1) |
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Linearization of Nonlinear Models |
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198 | (2) |
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Validation of Model Behavior against Experiment |
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200 | (1) |
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Model Based Noise Reduction and Feature Extraction |
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200 | (9) |
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Time Invariant System with Measurable Input-Output |
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201 | (2) |
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Time-Invariant System with Unknown Input |
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203 | (2) |
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Time Varying System with Measurable Input-Output |
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205 | (1) |
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Time Varying System with Unknown Input |
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206 | (1) |
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207 | (2) |
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Modeling the Nerve Action Potential |
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209 | (26) |
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Electrical Behavior of Excitable Tissue |
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209 | (7) |
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Excitation of Nerves: The Action Potential |
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210 | (1) |
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Extracellular and Intracellular Compartments |
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211 | (1) |
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211 | (2) |
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Electrical Equivalent of the Nerve Membrane |
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213 | (3) |
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The Voltage Clamp Experiment |
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216 | (4) |
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Opening the Feedback Loop of the Membrane |
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217 | (1) |
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Results of the Hodgkin-Huxley Experiments |
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218 | (2) |
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Interpreting the Voltage-Clamp Experimental Data |
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220 | (8) |
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Step Responses of the Ionic Conductances |
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220 | (1) |
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Hodgkin and Huxley's Nonlinear Model |
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221 | (4) |
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The Voltage Dependent Membrane Constants |
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225 | (1) |
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Simulation of the Hodgkin-Huxley Model |
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226 | (2) |
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A Model for the Strength-Duration Curve |
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228 | (7) |
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230 | (1) |
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231 | (4) |
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Modeling Skeletal Muscle Contraction |
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235 | (32) |
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Skeletal Muscle Contraction |
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235 | (1) |
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Properties of Skeletal Muscle |
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236 | (7) |
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Isometric Properties of Skeletal Muscle |
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237 | (3) |
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The Sliding Filament Hypothesis |
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240 | (1) |
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The Sarcomere as the Unit of Muscle Contraction |
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241 | (2) |
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The Cross-Bridge Theory of Muscle Contraction |
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243 | (12) |
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The Molecular Force Generator |
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245 | (2) |
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Isotonic Experiments and the Force-Velocity curve |
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247 | (3) |
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Huxley's Model of Isotonic Muscle Contraction |
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250 | (5) |
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A Linear Model of Muscle Contraction |
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255 | (5) |
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Linear Approximation of the Force-Velocity Curve |
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255 | (1) |
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A Mechanical Analogue Model for Muscle |
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255 | (5) |
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Applications of Skeletal Muscle Modeling |
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260 | (7) |
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A Model of Intrafusal Muscle Fibers |
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260 | (2) |
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Other Applications of Muscle Modeling |
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262 | (1) |
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263 | (1) |
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264 | (3) |
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Modeling Myoelectric Activity |
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267 | (28) |
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267 | (5) |
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Functional Organization of Skeletal Muscle |
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268 | (1) |
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268 | (4) |
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A Model of the Electromyogram |
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272 | (23) |
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Bipolar Recording Filter Function |
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275 | (4) |
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279 | (4) |
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283 | (6) |
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289 | (2) |
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291 | (4) |
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System Identification in Physiology |
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295 | (14) |
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Black Box Modeling of Physiological Systems |
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295 | (1) |
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295 | (8) |
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Firing Rate-Demodulation of Frequency Coding |
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296 | (5) |
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Estimating Receptor Transfer Function |
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301 | (2) |
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303 | (6) |
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303 | (3) |
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Estimating the Loop Transfer Function |
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306 | (1) |
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Instability of the Pupil Controller |
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306 | (1) |
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Applications of System Identification in Physiology |
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307 | (1) |
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307 | (2) |
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Modeling the Cardiovascular System |
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309 | (12) |
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309 | (9) |
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311 | (1) |
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Electrical Analogue of Flow in Vessels |
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311 | (3) |
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Simple Model of Systemic Blood Flow |
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314 | (3) |
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Modeling Coronary Circulation |
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317 | (1) |
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Other Applications of Cardiovascular Modeling |
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318 | (3) |
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319 | (2) |
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A Model of the Immune Response to Disease |
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321 | (8) |
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Behavior of the Immune System |
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321 | (2) |
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Linearized Model of the Immune Response |
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323 | (6) |
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System Equations for the Immune Response |
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325 | (1) |
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326 | (1) |
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327 | (1) |
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328 | (1) |
Appendix |
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329 | (2) |
Bibliography |
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331 | (4) |
Index |
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335 | |