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Modeling, Estimation and Optimal Filtration in Signal Processing

Book Description

The purpose of this book is to provide graduate students and practitioners with traditional methods and more recent results for model-based approaches in signal processing.

Firstly, discrete-time linear models such as AR, MA and ARMA models, their properties and their limitations are introduced. In addition, sinusoidal models are addressed.

Secondly, estimation approaches based on least squares methods and instrumental variable techniques are presented.

Finally, the book deals with optimal filters, i.e. Wiener and Kalman filtering, and adaptive filters such as the RLS, the LMS and their variants.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Table of Contents
  5. Preface
  6. Chapter 1: Parametric Models
    1. 1.1. Introduction
    2. 1.2. Discrete linear models
    3. 1.3. Observations on stability, stationarity and invertibility
    4. 1.4. The AR model or the ARMA model?
    5. 1.5. Sinusoidal models
    6. 1.6. State space representations
    7. 1.7. Conclusion
    8. 1.8. References
  7. Chapter 2: Least Squares Estimation of Parameters of Linear Models
    1. 2.1. Introduction
    2. 2.2. Least squares estimation of AR parameters
    3. 2.3. Selecting the order of the models
    4. 2.4. References
  8. Chapter 3: Matched and Wiener Filters
    1. 3.1. Introduction
    2. 3.2. Matched filter
    3. 3.3. The Wiener filter
    4. 3.4. References
  9. Chapter 4: Adaptive Filtering
    1. 4.1. Introduction
    2. 4.2. Recursive least squares algorithm
    3. 4.3. The least mean squares algorithm
    4. 4.4. Variants of the LMS algorithm
    5. 4.5. Summary of the properties of the different adaptive filters
    6. 4.6. Application: noise cancellation
    7. 4.7. References
  10. Chapter 5: Kalman Filtering
    1. 5.1. Introduction
    2. 5.2. Derivation of the Kalman filter
    3. 5.3. Application of the Kalman filter to parameter estimation
    4. 5.4. Nonlinear estimation
    5. 5.5. Conclusion
    6. 5.6. References
  11. Chapter 6: Application of the Kalman Filter to Signal Enhancement
    1. 6.1. Introduction
    2. 6.2. Enhancement of a speech signal disturbed by a white noise
    3. 6.3. Kalman filter-based enhancement of a signal disturbed by a colored noise
    4. 6.4. Conclusion
    5. 6.5. References
  12. Chapter 7: Estimation using the Instrumental Variable Technique
    1. 7.1. Introduction
    2. 7.2. Introduction to the instrumental variable technique
    3. 7.3. Kalman filtering and the instrumental variable method
    4. 7.4. Case study
    5. 7.5. Conclusion
    6. 7.6. References
  13. Chapter 8: H∞ Estimation: an Alternative to Kalman Filtering?
    1. 8.1. Introduction
    2. 8.2. Introduction to H∞ estimation
    3. 8.3. Estimation of AR parameters using H∞ filtering
    4. 8.4. Relevance of H∞ filtering to speech enhancement
    5. 8.5. Conclusion
    6. 8.6. References
  14. Chapter 9: Introduction to Particle Filtering
    1. 9.1. Monte Carlo methods
    2. 9.2. Sequential importance sampling filter
    3. 9.3. Review of existing particle filtering techniques
    4. 9.4. References
  15. Appendix A: Karhunen Loeve Transform
  16. Appendix B: Subspace Decomposition for Spectral Analysis
    1. References
  17. Appendix C: Subspace Decomposition Applied to Speech Enhancement
    1. References
  18. Appendix D: From AR Parameters to Line Spectrum Pair
  19. Appendix E: Influence of an Additive White Noise on the Estimation of AR Parameters
    1. References
  20. Appendix F: The Schur-Cohn Algorithm
    1. References
  21. Appendix G: The Gradient Method
  22. Appendix H: An Alternative Way of Understanding Kalman Filtering
    1. References
  23. Appendix I: Calculation of the Kalman Gain using the Mehra Approach
  24. Appendix J: Calculation of the Kalman Gain (the Carew and Belanger Method)
    1. References
  25. Appendix K: The Unscented Kalman Filter (UKF)
    1. References
  26. Index