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5.5 The Frequency Response of Continuous-Time LTI Systems 223
5.6 Filtering 227
5.7 Bandwidth 230
Solved Problems 231

Chapter 6. Fourier Analysis of Discrete-Time Signals and Systems 288
6.1 Introduction 288
6.2 Discrete Fourier Series 288
6.3 The Fourier Transform 291
6.4 Properties of the Fourier Transform 295
6.5 The Frequency Response of Discrete-Time LTI Systems 300
6.6 System Response to Sampled Continuous-Time Sinusoids 302
6.7 Simulation 303
6.8 The Discrete Fourier Transform 305
Solved Problems 308
Chapter 7. State Space Analysis 365
7.1 Introduction 365
7.2 The Concept of State 365
7.3 State Space Representation of Discrete-Time LTI Systems 366
7.4 State Space Representation of Continuous-Time LTI Systems 368
7.5 Solutions of State Equations for Discrete-Time LTI Systems 371
7.6 Solutions of State Equations for Continuous-Time LTI Systems 374
Solved Problems 377

Appendix A. Review of Matrix Theory 428
A.1 Matrix Notation and Operations 428
A.2 Transpose and Inverse 431
A.3 Linear Independence and Rank 432
A.4 Determinants 433
A.5 Eigenvalues and Eigenvectors 435
A.6 Diagonalization and Similarity Transformation 436
A.7 Functions of a Matrix 437
A.8 Differentiation and Integration of Matrices 444

Appendix B. Properties of Linear Time-Invariant Systems and Various Transforms 445
B.1 Continuous-Time LTI Systems 445
B.2 The Laplace Transform 445
B.3 The Fourier Transform 447
B.4 Discrete-Time LTI Systems 449
B.5 The z-Transform 449
B.6 The Discrete-Time Fourier Transform 451
B.7 The Discrete Fourier Transform 452
B.8 Fourier Series 453
B.9 Discrete Fourier Series 454

Appendix C. Review of Complex Numbers 455
C.1 Representation of Complex Numbers 455
C.2 Addition, Multiplication, and Division 456
C.3 The Complex Conjugate 456
C.4 Powers and Roots of Complex Numbers 456
Appendix D. Useful Mathematical Formulas 458
D.1 Summation Formulas 458
D.2 Euler's Formulas 458

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