Identification of nonlinear physiological systems /

Identification of nonlinear physiological systems /

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Bibliographic Details
Author / Creator:Westwick, David T.
Imprint:[Piscataway, N.J.?] : IEEE Press ; Hoboken, NJ : Wiley-Interscience, c2003.
Description:1 online resource (xii, 261 p.) : ill.
Language:English
Series:IEEE Press series on biomedical engineering
IEEE Press series in biomedical engineering.
Subject:
Physiology -- Mathematical models.
Nonlinear systems.
Nonlinear systems.
Physiology -- Mathematical models.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8680103
Hidden Bibliographic Details
Other authors / contributors:Kearney, Robert E., 1947-
IEEE Engineering in Medicine and Biology Society.
John Wiley & Sons.
ISBN:0471274569 (cloth)
9780471274568 (cloth)
0471722960 (electronic bk.)
9780471722960 (electronic bk.)
Notes:"IEEE Engineering in Medicine and Biology Society, Sponsor."
Includes bibliographical references (p. 251-257) and index.
Other form:Print version: Westwick, David T. Identification of nonlinear physiological systems. [Piscataway, N.J.?] : IEEE Press ; Hoboken, NJ : Wiley-Interscience, c2003 0471274569
Standard no.:10.1002/0471722960
Table of Contents:
  • Preface
  • 1. Introduction
  • 1.1. Signals
  • 1.1.1. Domain and Range
  • 1.1.2. Deterministic and Stochastic Signals
  • 1.1.3. Stationary and Ergodic Signals
  • 1.2. Systems and Models
  • 1.2.1. Model Structure and Parameters
  • 1.2.2. Static and Dynamic Systems
  • 1.2.3. Linear and Nonlinear Systems
  • 1.2.4. Time-Invariant and Time-Varying Systems
  • 1.2.5. Deterministic and Stochastic Systems
  • 1.3. System Modeling
  • 1.4. System Identification
  • 1.4.1. Types of System Identification Problems
  • 1.4.2. Applications of System Identification
  • 1.5. How Common are Nonlinear Systems?
  • 2. Background
  • 2.1. Vectors and Matrices
  • 2.2. Gaussian Random Variables
  • 2.2.1. Products of Gaussian Variables
  • 2.3. Correlation Functions
  • 2.3.1. Autocorrelation Functions
  • 2.3.2. Cross-Correlation Functions
  • 2.3.3. Effects of Noise
  • 2.3.4. Estimates of Correlation Functions
  • 2.3.5. Frequency Domain Expressions
  • 2.3.6. Applications
  • 2.3.7. Higher-Order Correlation Functions
  • 2.4. Mean-Square Parameter Estimation
  • 2.4.1. Linear Least-Squares Regression
  • 2.4.2. Properties of Estimates
  • 2.5. Polynomials
  • 2.5.1. Power Series
  • 2.5.2. Orthogonal Polynomials
  • 2.5.3. Hermite Polynomials
  • 2.5.4. Tchebyshev Polynomials
  • 2.5.5. Multiple-Variable Polynomials
  • 2.6. Notes and References
  • 2.7. Problems
  • 2.8. Computer Exercises
  • 3. Models of Linear Systems
  • 3.1. Linear Systems
  • 3.2. Nonparametric Models
  • 3.2.1. Time Domain Models
  • 3.2.2. Frequency Domain Models
  • 3.3. Parametric Models
  • 3.3.1. Parametric Frequency Domain Models
  • 3.3.2. Discrete-Time Parametric Models
  • 3.4. State-Space Models
  • 3.4.1. Example: Human Ankle Compliance--Discrete-Time, State-Space Model
  • 3.5. Notes and References
  • 3.6. Theoretical Problems
  • 3.7. Computer Exercises
  • 4. Models of Nonlinear Systems
  • 4.1. The Volterra Series
  • 4.1.1. The Finite Volterra Series
  • 4.1.2. Multiple-Input Systems
  • 4.1.3. Polynomial Representation
  • 4.1.4. Convergence Issues
  • 4.2. The Wiener Series
  • 4.2.1. Orthogonal Expansion of the Volterra Series
  • 4.2.2. Relation Between the Volterra and Wiener Series
  • 4.2.3. Example: Peripheral Auditory Model--Wiener Kernels
  • 4.2.4. Nonwhite Inputs
  • 4.3. Simple Block Structures
  • 4.3.1. The Wiener Model
  • 4.3.2. The Hammerstein Model
  • 4.3.3. Sandwich or Wiener-Hammerstein Models
  • 4.3.4. NLN Cascades
  • 4.3.5. Multiple-Input Multiple-Output Block Structured Models
  • 4.4. Parallel Cascades
  • 4.4.1. Approximation Issues
  • 4.5. The Wiener-Bose Model
  • 4.5.1. Similarity Transformations and Uniqueness
  • 4.5.2. Approximation Issues
  • 4.5.3. Volterra Kernels of the Wiener-Bose Model
  • 4.5.4. Wiener Kernels of the Wiener-Bose Model
  • 4.5.5. Relationship to the Parallel Cascade Model
  • 4.6. Notes and References
  • 4.7. Theoretical Problems
  • 4.8. Computer Exercises
  • 5. Identification of Linear Systems
  • 5.1. Introduction
  • 5.1.1. Example: Identification of Human Joint Compliance
  • 5.1.2. Model Evaluation
  • 5.2. Nonparametric Time Domain Models
  • 5.2.1. Direct Estimation
  • 5.2.2. Least-Squares Regression
  • 5.2.3. Correlation-Based Methods
  • 5.3. Frequency Response Estimation
  • 5.3.1. Sinusoidal Frequency Response Testing
  • 5.3.2. Stochastic Frequency Response Testing
  • 5.3.3. Coherence Functions
  • 5.4. Parametric Methods
  • 5.4.1. Regression
  • 5.4.2. Instrumental Variables
  • 5.4.3. Nonlinear Optimization
  • 5.5. Notes and References
  • 5.6. Computer Exercises
  • 6. Correlation-Based Methods
  • 6.1. Methods for Functional Expansions
  • 6.1.1. Lee-Schetzen Cross-Correlation
  • 6.1.2. Colored Inputs
  • 6.1.3. Frequency Domain Approaches
  • 6.2. Block-Structured Models
  • 6.2.1. Wiener Systems
  • 6.2.2. Hammerstein Models
  • 6.2.3. LNL Systems
  • 6.3. Problems
  • 6.4. Computer Exercises
  • 7. Explicit Least-Squares Methods
  • 7.1. Introduction
  • 7.2. The Orthogonal Algorithms
  • 7.2.1. The Orthogonal Algorithm
  • 7.2.2. The Fast Orthogonal Algorithm
  • 7.2.3. Variance of Kernel Estimates
  • 7.2.4. Example: Fast Orthogonal Algorithm Applied to Simulated Fly Retina Data
  • 7.2.5. Application: Dynamics of the Cockroach Tactile Spine
  • 7.3. Expansion Bases
  • 7.3.1. The Basis Expansion Algorithm
  • 7.3.2. The Laguerre Expansion
  • 7.3.3. Limits on [alpha]
  • 7.3.4. Choice of [alpha] and P
  • 7.3.5. The Laguerre Expansion Technique
  • 7.3.6. Computational Requirements
  • 7.3.7. Variance of Laguerre Kernel Estimates
  • 7.3.8. Example: Laguerre Expansion Kernels of the Fly Retina Model
  • 7.4. Principal Dynamic Modes
  • 7.4.1. Example: Principal Dynamic Modes of the Fly Retina Model
  • 7.4.2. Application: Cockroach Tactile Spine
  • 7.5. Problems
  • 7.6. Computer Exercises
  • 8. Iterative Least-Squares Methods
  • 8.1. Optimization Methods
  • 8.1.1. Gradient Descent Methods
  • 8.1.2. Identification of Block-Structured Models
  • 8.1.3. Second-Order Optimization Methods
  • 8.1.4. Jacobians for Other Block Structures
  • 8.1.5. Optimization Methods for Parallel Cascade Models
  • 8.1.6. Example: Using a Separable Volterra Network
  • 8.2. Parallel Cascade Methods
  • 8.2.1. Parameterization Issues
  • 8.2.2. Testing Paths for Significance
  • 8.2.3. Choosing the Linear Elements
  • 8.2.4. Parallel Wiener Cascade Algorithm
  • 8.2.5. Longer Cascades
  • 8.2.6. Example: Parallel Cascade Identification
  • 8.3. Application: Visual Processing in the Light-Adapted Fly Retina
  • 8.4. Problems
  • 8.5. Computer Exercises
  • References
  • Index
  • IEEE Press Series in Biomedical Engineering

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