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An Operator Perspective on Signals and Systems

  • Arthur E. Frazho
  • Wisuwat Bhosri

Part of the Operator Theory: Advances and Applications book series (OT, volume 204)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Basic Operator Theory

    1. Front Matter
      Pages 1-1
    2. Arthur E. Frazho, Wisuwat Bhosri
      Pages 3-22
    3. Arthur E. Frazho, Wisuwat Bhosri
      Pages 23-40
    4. Arthur E. Frazho, Wisuwat Bhosri
      Pages 41-53
    5. Arthur E. Frazho, Wisuwat Bhosri
      Pages 55-90
    6. Arthur E. Frazho, Wisuwat Bhosri
      Pages 91-116
    7. Arthur E. Frazho, Wisuwat Bhosri
      Pages 117-141
  3. Finite Section Techniques

    1. Front Matter
      Pages 143-143
    2. Arthur E. Frazho, Wisuwat Bhosri
      Pages 145-178
    3. Arthur E. Frazho, Wisuwat Bhosri
      Pages 179-208
    4. Arthur E. Frazho, Wisuwat Bhosri
      Pages 209-244
  4. Riccati Methods

    1. Front Matter
      Pages 245-245
    2. Arthur E. Frazho, Wisuwat Bhosri
      Pages 247-282
    3. Arthur E. Frazho, Wisuwat Bhosri
      Pages 283-314
  5. Interpolation Theory

    1. Front Matter
      Pages 315-315
    2. Arthur E. Frazho, Wisuwat Bhosri
      Pages 317-339
    3. Arthur E. Frazho, Wisuwat Bhosri
      Pages 341-371
  6. Appendices

    1. Front Matter
      Pages 373-373
    2. Arthur E. Frazho, Wisuwat Bhosri
      Pages 375-397
    3. Arthur E. Frazho, Wisuwat Bhosri
      Pages 399-412
  7. Back Matter
    Pages 413-429

About this book

Introduction

In this monograph, we combine operator techniques with state space methods to solve factorization, spectral estimation, and interpolation problems arising in control and signal processing. We present both the theory and algorithms with some Matlab code to solve these problems. A classical approach to spectral factorization problems in control theory is based on Riccati equations arising in linear quadratic control theory and Kalman ?ltering. One advantage of this approach is that it readily leads to algorithms in the non-degenerate case. On the other hand, this approach does not easily generalize to the nonrational case, and it is not always transparent where the Riccati equations are coming from. Operator theory has developed some elegant methods to prove the existence of a solution to some of these factorization and spectral estimation problems in a very general setting. However, these techniques are in general not used to develop computational algorithms. In this monograph, we will use operator theory with state space methods to derive computational methods to solve factorization, sp- tral estimation, and interpolation problems. It is emphasized that our approach is geometric and the algorithms are obtained as a special application of the theory. We will present two methods for spectral factorization. One method derives al- rithms based on ?nite sections of a certain Toeplitz matrix. The other approach uses operator theory to develop the Riccati factorization method. Finally, we use isometric extension techniques to solve some interpolation problems.

Keywords

Factorization Filtering Interpolation Levinson algorithm MATLAB Operator theory Riccati equation Signal processing State space

Authors and affiliations

  • Arthur E. Frazho
    • 1
  • Wisuwat Bhosri
    • 2
  1. 1.School of Aeronautics and AstronauticsPurdue UniversityWest LafayetteUSA
  2. 2.Chiang MaiThailand

Bibliographic information