Principles of Neurobiological Signal Analysis

PrefaceChapter 1: Some Properties of Biological Signals 1.1 Introduction 1.2 Continuous Signals and Their Discrete Counterparts 1.3 Repetitive and Periodic Signals 1.4 Sampled Representation of a Signal 1.5 Fourier Series Representation of a Signal 1.6 Bandwidth Limited Signals 1.7 Autocovariance Functions and Power Spectra of Periodic Signals 1.8 Aperiodic Signals 1.9 Autocovariance Functions and Power Spectra of Aperiodic Signals 1.10 Cross Covariance Functions and Cross Spectra for a Pair of Periodic Signals 1.11 A Summary of Properties of Covariance Functions and Spectra 1.12 Random or Probabilistic Signals 1.13 Some Important Probability Distributions A. Probabilistic Descriptions of Dynamic Processes B. The Gaussian Distribution C. The Chi-Squared Distribution 1.14 Ensemble Autocovariance Functions 1.15 Ensemble Autocovariance and Cross Covariance Functions, and Stationarity 1.16 The Relationship between Ensemble and Time Statistics 1.17 Mixtures of Signal and Nois 1.18 Response Detection and Classification - Hypothesis TestingChapter 2 Basics of Signal Processing 2.1 Introduction 2.2 Analog-to Digital Conversion 2.3 Quantization Noise 2.4 Multiplexing: Monitoring Data Sources Simultaneously 2.5 Data Filtering 2.6 The Digital Filter A. Filtering of the Constant Component B. Filtering the/mth Frequency Component 2.7 Impulse Response of a Digital Filter 2.8 Spectral Relations between Filter Input and Output-The Discrete Fourier Transform 2.9 Filtering Aperiodic Signals A. Short Duration Signals ¿. Maintained Signals 2.10 Data Smoothing by Digital Filtering 2.11 Digital Filters with Feedback - Recursive Filters 2.12 The Linear Analog Filter 2.13 The Laplace Transform, the Filter Transfer Function, and Impulse Response 2.14 The Operational Amplifier 2.15 The Amplitude Comparator 2.16 Time-Varying and Nonlinear Filters 100Chapter 3: Power Spectra and Covariance Functions 3.1 Introduction 3.2 Discrete Fourier Representations of Continuous Processes 3.3 Aliasing 3.4 Leakage A. Fourier Series B. Discrete Fourier Transforms 3.5 Trend 3.6 The Power Spectrum, General Considerations 3.7 Power Spectrum of Continuous Random Signals 3.8 The Power Spectrum of T-Discrete Signals 3.9 The Fourier Transform for T-Discrete Signals 3.10 The Periodogram 3.11 Statistical Errors of the Periodogram-Bias 3.12 Statistical Errors of the Periodogram-Variance 3.13 Averaging the Periodogram the Bartlett Estimator 3.14 Variance of the Bartlett Estimator 3.15 The Fast Fourier Transform and Power Spectrum Estimation 3.16 Smoothing of Spectral Estimates by Windowing 3.17 The Cross Spectrum 3.18 Covariance Functions A. Some Statistical Properties of the ACVF Estimators B. Estimation of the ACVF C. Cross Covariance Function Estimation 3.19 Coherence Functions 3.20 Phase EstimationChapter 4: Evoked Potentials: Averaging and Discriminant Analysis 4.1 Introduction 4.2 Estimation of Variability 4.3 Confidence Intervals 4.4 Comments on Assumptions 4.5 Alternative Measures of Variability A. Split Sweep Assessment of Significance B. Plus-Minus Reference Method 4.6 Correlated Noise, Overlap and Stimulus Spacing A. Aperiodic Stimuli B. Narrow Band Noise and Aperiodic Stimuli 4.7 The Median Evoked Response 4.8 Nonhomogeneous Sets of Evoked Potentials 4.9 Correlation Estimation of a Constant Waveform with Varying Latency 4.10 Homogeneous Subsets 4.11 The Cumsum Procedure A. The Precum Method B. Distribution of Precums for Homogeneous Responses C. An Algorithm for Computing Precum 4.12 The Sort Method 4.13 Discriminant Analysis 4.