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| Preface | |
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| The Nature of Biomedical Signals | |
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| The Reasons for Studying Biomedical Signal Processing | |
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| What Is a Signal? | |
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| Some Typical Sources of Biomedical Signals | |
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| Continuous-Time and Discrete-Time | |
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| Assessing the Relationships Between Two Signals | |
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| Why Do We "Process" Signals? | |
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| Types of Signals: Deterministic, Stochastic, Fractal and Chaotic | |
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| Signal Modeling as a Framework for Signal Processing | |
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| What Is Noise? | |
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| Summary | |
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| Exercises | |
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| Memory and Correlation | |
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| Introduction | |
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| Properties of Operators and Transformations | |
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| Memory in a Physical System | |
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| Energy and Power Signals | |
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| The Concept of Autocorrelation | |
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| Autocovariance and Autocorrelation for DT Signals | |
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| Summary | |
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| Exercises | |
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| The Impulse Response | |
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| Introduction | |
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| Thought Experiment and Computer Exercise: Glucose Control | |
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| Convolution Form of an LSI System | |
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| Convolution for Continuous-Time Systems | |
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| Convolution as Signal Processing | |
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| Relation of Impulse Response to Differential Equation | |
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| Convolution as a Filtering Process | |
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| Impulse Responses for Nonlinear Systems | |
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| The Glucose Control Problem Revisited | |
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| Summary | |
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| Exercises | |
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| Frequency Response | |
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| Introduction | |
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| Biomedical Example (Transducers for Measuring Knee Angle) | |
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| Sinusoidal Inputs to LTIC Systems | |
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| Generalized Frequency Response | |
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| Frequency Response of Discrete-Time Systems | |
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| Series and Parallel Filter Cascades | |
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| Ideal Filters | |
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| Frequency Response and Nonlinear Systems | |
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| Other Biomedical Examples | |
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| Summary | |
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| Exercises | |
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| Modeling Continuous-Time Signals as Sums of Sine Waves | |
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| Introduction | |
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| Introductory Example (Analysis of Circadian Rhythm) | |
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| Orthogonal Functions | |
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| Sinusoidal Basis Functions | |
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| The Fourier Series | |
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| The Frequency Response and Nonsinusoidal Periodic Inputs | |
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| Parseval's Relation for Periodic Signals | |
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| The Continuous-Time Fourier Transform (CTFT) | |
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| Relationship of Fourier Transform to Frequency Response | |
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| Properties of the Fourier Transform | |
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| The Generalized Fourier Transform | |
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| Examples of Fourier Transform Calculations | |
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| Parseval's Relation for Nonperiodic Signals | |
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| Filtering | |
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| Output Response via the Fourier Transform | |
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| Summary | |
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| Exercises | |
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| Responses of Linear Continuous-Time Filters to Arbitrary Inputs | |
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| Introduction | |
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| Introductory Example | |
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| Conceptual Basis of the Laplace Transform | |
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| Properties of (Unilateral) Laplace Transforms | |
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| The Inverse (Unilateral) Laplace Transform | |
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| Transfer Functions | |
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| Feedback Systems | |
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| Biomedical Applications of Laplace Transforms | |
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| Summary | |
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| Exercises | |
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| Modeling Signals as Sums of Discrete-Time Sine Waves | |
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| Introduction | |
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| Interactive Example: Periodic Oscillations in the Amplitude of Breathing | |
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| The Discrete-Time Fourier Series | |
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| Fourier Transform of Discrete-Time Signals | |
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| Parseval's Relation for DT Nonperiodic Signals | |
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| Output of an LSI System | |
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| Relation of DFS and DTFT | |
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| Windowing | |
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| Sampling | |
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| The Discrete Fourier Transform (DFT) | |
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| Biomedical Applications | |
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| Summary | |
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| Exercises | |
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| Noise Removal and Signal Compensation | |
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| Introduction | |
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| Introductory Example: Reducing the ECG Artifact in an EMG Recording | |
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| Eigenfunctions of LSI Systems and the Z-Transform | |
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| Properties of the Bilateral Z-Transform | |
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| Poles and Zeros of Z-Transforms | |
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| The Inverse Z-Transform | |
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| Pole Locations and Time Responses | |
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| The Unilateral Z-Transform | |
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| Analyzing Digital Filters Using Z-Transforms (DT Transfer Functions) | |
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| Biomedical Applications of DT Filters | |
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| Overview: Design of Digital Filters | |
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| IIR Filter Design by Approximating a CT Filter | |
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| IIR Filter Design by Impulse Invariance | |
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| IIR Filter Design by Bilinear Transformation | |
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| Biomedical Examples of IIR Digital Filter Design | |
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| IIR Filter Design by Minimization of an Error Function | |
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| FIR Filter Design | |
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| Frequency-Band Transformations | |
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| Biomedical Applications of Digital Filtering | |
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| Summary | |
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| Exercises | |
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| Modeling Stochastic Signals as Filtered White Noise | |
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| Introduction | |
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| Introductory Exercise: EEG Analysis | |
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| Random Processes | |
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| Mean and Autocorrelation Function of a Random Process | |
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| Stationarity and Ergodicity | |
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| General Linear Processes | |
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| Yule-Walker Equations | |
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| Autoregressive (AR) Processes | |
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| Moving Average (MA) Processes | |
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| Autoregressive-Moving Average (ARMA) Processes | |
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| Harmonic Processes | |
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| Other Biomedical Examples | |
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| Introductory Example Continued | |
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| Summary | |
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| Exercises | |
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| Scaling and Long-Term Memory | |
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| Introduction | |
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| Geometrical Scaling and Self-Similarity | |
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| Measures of Dimension | |
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| Self-Similarity and Functions of Time | |
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| Theoretical Signals Having Statistical Similarity | |
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| Measures of Statistical Similarity for Real Signals | |
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| Generation of Synthetic Fractal Signals | |
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| Fractional Differencing Models | |
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| Biomedical Examples | |
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| Summary | |
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| Exercises | |
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| Nonlinear Models of Signals | |
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| Introductory Exercise | |
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| Nonlinear Signals and Systems: Basic Concepts | |
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| Poincare Sections and Return Maps | |
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| Chaos | |
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| Measures of Nonlinear Signals and Systems | |
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| Characteristic Multipliers and Lyapunov Exponents | |
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| Estimating the Dimension of Real Data | |
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| Tests of Null Hypotheses Based on Surrogate Data | |
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| Other Biomedical Applications | |
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| Summary | |
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| Exercises | |
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| Assessing Stationarity and Reproducibility | |
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| Introduction | |
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| Assessing Stationarity of a Random Process from a Sample Function | |
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| Statistical Properties of Autocovariance Estimators | |
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| Statistical Properties of the Periodogram | |
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| Analysis of Nonstationary Signals | |
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| Nonstationary Second-Order Statistics | |
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| Summary | |
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| Exercises | |
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| Bibliography | |
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| Index | |