An operator perspective on signals and systems

303460291X......Page 1
An Operator Perspective on Signals and Systems......Page 4
Preface......Page 6
Contents......Page 8
I Basic Operator Theory......Page 13
1 The Wold Decomposition......Page 14
2 Toeplitz and Laurent Operators......Page 34
3 Inner and Outer Functions......Page 52
4 Rational Inner and Outer Functions......Page 65
5 The Naimark Representation......Page 101
6 The Rational Case......Page 127
II Finite Section Tec......Page 152
7 The Levinson Algorithm and Factorization......Page 153
8 Isometric Representations and......Page 187
9 Signal Processing......Page 217
III Riccati Methods......Page 253
10 Riccati Equations and Factorization......Page 254
11 Kalman and Wiener Filtering......Page 290
IV Interpolation Theory......Page 322
12 Tangential Nevanlinna-Pick Interpolation......Page 323
13 Contractive Nevanlinna-Pick Interpolation......Page 346
V Appendices......Page 377
14 A Review of State Space......Page 378
15 The Levinson Algorithm......Page 401
Bibliography......Page 415
Index......Page 428