Table of Contents

  • 1. Introduction
    • 1.1. Examples of Central Problems
    • 1.2. Signal Representation
    • 1.3. Basic Tools
    • 1.4. Outline of the Book
    • 1.5. Summary
    • 1.6. Bibliography
  • 2. Frequency Models
    • 2.1. Introduction
    • 2.2. Frequency Models for Continuous-Time Signals
    • 2.3. Discrete Time Fourier Transform 
    • 2.4. Information Loss due to Sampling
    • 2.5. Information Loss due to Truncation
    • 2.6. The Discrete Fourier Transform
    • 2.7. DFT Applications
    • 2.8. Practical Aspects
    • 2.9. Summary
    • 2.10. Bibliography
    • 2.A. Distributions and Fourier Transforms
  • 3. Stochastic Signals and Spectral Models
    • 3.1. Introduction
    • 3.2. Stochastic Processes
    • 3.3. Spectrum
    • 3.4. Estimation of Covariance Functions
    • 3.5. Estimation of Spectra
    • 3.6. Summary
    • 3.7. Bibliography
  • 4. Filtering
    • 4.1. Introduction
    • 4.2. Linear Filters
    • 4.3. The Signal and Noise Problem
    • 4.4. Specifications on Frequency Selective Filters
    • 4.5. Construction of Digital Filters
    • 4.6. Choice of Filter
    • 4.7. Implementation of Filters
    • 4.8. Summary
    • 4.9. Bibliography
  • 5. Signal Models
    • 5.1. Introduction
    • 5.2. Signal Models as Filtered White Noise
    • 5.3. Signal Models with Several Signals
    • 5.4. AR and ARMA Models
    • 5.5. State Space Models
    • 5.6. Prediction
    • 5.7. Summary
    • 5.8. Bibliography
  • 6. Model Estimation
    • 6.1. Introduction
    • 6.2. Estimation of Linear Models
    • 6.3. Estimation of AR Models
    • 6.4. Estimation of Nonlinear Models
    • 6.5. Estimation of ARMA Models
    • 6.6. Practical Aspects
    • 6.7. Summary
    • 6.8. Bibliography
  • 7. Wiener Filtering
    • 7.1. Introduction
    • 7.2. Wiener’s Problem Formulation
    • 7.3. The Wiener–Hopf Equations
    • 7.4. The FIR Wiener Filter
    • 7.5. The Non-Causal Wiener Filter
    • 7.6. Tracking using the Wiener Filter
    • 7.7. The Causal Wiener Filter
    • 7.8. Wiener Filter Residual Variance
    • 7.9. Wiener Filter for Models with One Noise Source
    • 7.10. Summary
    • 7.11. Bibliography
  • 8. Kalman Filtering
    • 8.1. Introduction
    • 8.2. The Kalman Filter
    • 8.3. Stationary Kalman Filter
    • 8.4. Relations Between the Kalman and Wiener Filters
    • 8.5. Smoothing and Prediction
    • 8.6. Square Root Implementation
    • 8.7. Summary
    • 8.8. Bibliography
  • 9. Adaptive Filtering
    • 9.1. Introduction
    • 9.2. Signal Models
    • 9.3. Adaptive Algorithms
    • 9.4. Change Detection
    • 9.5. A Simulation Example
    • 9.6. Noise Cancelation
    • 9.7. Summary
    • 9.8. Bibliography
    • 9.A. Performance Analysis
  • Bibliograph