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## Table of contents

1. Preliminaries
2. Dedication
3. Preface
4. Chapter 1 Signal Representation and Modeling
1. Chapter Objectives
2. 1.1 Introduction
3. 1.2 Mathematical Modeling of Signals
4. 1.3 Continuous-Time Signals
1. 1.3.1 Signal operations
2. 1.3.2 Basic building blocks for continuous-time signals
3. 1.3.3 Impulse decomposition for continuous-time signals
4. 1.3.4 Signal classifications
5. 1.3.5 Energy and power definitions
6. 1.3.6 Symmetry properties
7. 1.3.7 Graphical representation of sinusoidal signals using phasors
5. 1.4 Discrete-Time Signals
1. 1.4.1 Signal operations
2. 1.4.2 Basic building blocks for discrete-time signals
3. 1.4.3 Impulse decomposition for discrete-time signals
4. 1.4.4 Signal classifications
5. 1.4.5 Energy and power definitions
6. 1.4.6 Symmetry properties
6. 1.5 Further Reading
7. MATLAB Exercises
8. Problems
9. MATLAB Problems
10. MATLAB Projects
5. Chapter 2 Analyzing Continuous-Time Systems in the Time Domain
1. Chapter Objectives
2. 2.1 Introduction
3. 2.2 Linearity and Time Invariance
4. 2.3 Differential Equations for Continuous-Time Systems
5. 2.4 Constant-Coefficient Ordinary Differential Equations
6. 2.5 Solving Differential Equations
7. 2.6 Block Diagram Representation of Continuous-Time Systems
8. 2.7 Impulse Response and Convolution
9. 2.8 Causality in Continuous-Time Systems
10. 2.9 Stability in Continuous-Time Systems
11. 2.10 Approximate Numerical Solution of a Differential Equation
12. 2.11 Further Reading
13. MATLAB Exercises
14. Problems
15. MATLAB Problems
16. MATLAB Projects
6. Chapter 3 Analyzing Discrete-Time Systems in the Time Domain
1. Chapter Objectives
2. 3.1 Introduction
3. 3.2 Linearity and Time Invariance
4. 3.3 Difference Equations for Discrete-Time Systems
5. 3.4 Constant-Coefficient Linear Difference Equations
6. 3.5 Solving Difference Equations
7. 3.6 Block Diagram Representation of Discrete-Time Systems
8. 3.7 Impulse Response and Convolution
9. 3.8 Causality in Discrete-Time Systems
10. 3.9 Stability in Discrete-Time Systems
11. 3.10 Further Reading
12. MATLAB Exercises
13. Problems
14. MATLAB Problems
15. MATLAB Projects
7. Chapter 4 Fourier Analysis for Continuous-Time Signals and Systems
1. Chapter Objectives
2. 4.1 Introduction
3. 4.2 Analysis of Periodic Continuous-Time Signals
1. 4.2.1 Approximating a periodic signal with trigonometric functions
2. 4.2.2 Trigonometric Fourier series (TFS)
3. 4.2.3 Exponential Fourier series (EFS)
4. 4.2.4 Compact Fourier series (CFS)
5. 4.2.5 Existence of Fourier series
6. 4.2.6 Gibbs phenomenon
7. 4.2.7 Properties of Fourier series
4. 4.3 Analysis of Non-Periodic Continuous-Time Signals
1. 4.3.1 Fourier transform
2. 4.3.2 Existence of Fourier transform
3. 4.3.3 Developing further insight
4. 4.3.4 Fourier transforms of some signals
5. 4.3.5 Properties of the Fourier transform
6. 4.3.6 Applying Fourier transform to periodic signals
5. 4.4 Energy and Power in the Frequency Domain
1. 4.4.1 Parseval’s theorem
2. 4.4.2 Energy and power spectral density
3. 4.4.3 Autocorrelation
6. 4.5 System Function Concept
7. 4.6 CTLTI Systems with Periodic Input Signals
8. 4.7 CTLTI Systems with Non-Periodic Input Signals
9. 4.8 Further Reading
10. MATLAB Exercises
11. Problems
12. MATLAB Problems
13. MATLAB Projects
8. Chapter 5 Fourier Analysis for Discrete-Time Signals and Systems
1. Chapter Objectives
2. 5.1 Introduction
3. 5.2 Analysis of Periodic Discrete-Time Signals
1. 5.2.1 Discrete-Time Fourier Series (DTFS)
2. 5.2.2 Properties of the DTFS
4. 5.3 Analysis of Non-Periodic Discrete-Time Signals
1. 5.3.1 Discrete-time Fourier transform (DTFT)
2. 5.3.2 Developing further insight
3. 5.3.3 Existence of the DTFT
4. 5.3.4 DTFT of some signals
5. 5.3.5 Properties of the DTFT
6. 5.3.6 Applying DTFT to periodic signals
5. 5.4 Energy and Power in the Frequency Domain
1. 5.4.1 Parseval’s theorem
2. 5.4.2 Energy and power spectral density
3. 5.4.3 Autocorrelation
6. 5.5 System Function Concept
7. 5.6 DTLTI Systems with Periodic Input Signals
8. 5.7 DTLTI Systems with Non-Periodic Input Signals
9. 5.8 Discrete Fourier Transform
1. 5.8.1 Relationship of the DFT to the DTFT
2. 5.8.2 Zero padding
3. 5.8.3 Properties of the DFT
4. 5.8.4 Using the DFT to approximate the EFS coefficients
5. 5.8.5 Using the DFT to approximate the continuous Fourier transform
10. 5.9 Further Reading
11. MATLAB Exercises
12. Problems
13. MATLAB Problems
14. MATLAB Projects
9. Chapter 6 Sampling and Reconstruction
1. Chapter Objectives
2. 6.1 Introduction
3. 6.2 Sampling of a Continuous-Time Signal
1. 6.2.1 Nyquist sampling criterion
2. 6.2.2 DTFT of sampled signal
3. 6.2.3 Sampling of sinusoidal signals
4. 6.2.4 Practical issues in sampling
4. 6.3 Reconstruction of a Signal from Its Sampled Version
5. 6.4 Resampling Discrete-Time Signals
6. 6.5 Further Reading
7. MATLAB Exercises
8. Problems
9. MATLAB Problems
10. MATLAB Projects
10. Chapter 7 Laplace Transform for Continuous-Time Signals and Systems
1. Chapter Objectives
2. 7.1 Introduction
3. 7.2 Characteristics of the Region of Convergence
4. 7.3 Properties of the Laplace Transform
5. 7.4 Inverse Laplace Transform
6. 7.5 Using the Laplace Transform with CTLTI Systems
1. 7.5.1 Relating the system function to the differential equation
2. 7.5.2 Response of a CTLTI system to a complex exponential signal
3. 7.5.3 Response of a CTLTI system to an exponentially damped sinusoid
4. 7.5.4 Pole-zero plot for a system function
5. 7.5.5 Graphical interpretation of the pole-zero plot
6. 7.5.6 System function and causality
7. 7.5.7 System function and stability
8. 7.5.8 Allpass systems
9. 7.5.9 Inverse systems
10. 7.5.10 Bode plots
7. 7.6. Simulation Structures for CTLTI Systems
8. 7.7 Unilateral Laplace Transform
9. 7.5 Further Reading
10. MATLAB Exercises
11. Problems
12. MATLAB Problems
13. MATLAB Projects
11. Chapter 8 z-Transform for Discrete-Time Signals and Systems
1. Chapter Objectives
2. 8.1 Introduction
3. 8.2 Characteristics of the Region of Convergence
4. 8.3 Properties of the z-Transform
5. 8.4 Inverse z-Transform
6. 8.5 Using the z-Transform with DTLTI Systems
7. 8.6 Implementation Structures for DTLTI Systems
8. 8.7 Unilateral z-Transform
9. 8.8 Further Reading
10. MATLAB Exercises
11. Problems
12. MATLAB Problems
13. MATLAB Project
12. Chapter 9 State-Space Analysis of Systems
1. Chapter Objectives
2. 9.1 Introduction
3. 9.2 State-Space Modeling of Continuous-Time Systems
4. 9.3 State-Space Modeling of Discrete-Time Systems
5. 9.4 Discretization of Continuous-Time State-Space Model
6. 9.5 Further Reading
7. MATLAB Exercises
8. Problems
9. MATLAB Problems
13. Chapter 10 Analysis and Design of Filters
1. Chapter Objectives
2. 10.1 Introduction
3. 10.2 Distortionless Transmission
4. 10.3 Ideal Filters
5. 10.4 Design of Analog Filters
1. 10.4.1 Butterworth lowpass filters
2. 10.4.2 Chebyshev lowpass filters
3. 10.4.3 Inverse Chebyshev lowpass filters
4. 10.4.4 Analog filter transformations
6. 10.5 Design of Digital Filters
1. 10.5.1 Design of IIR filters
2. 10.5.2 Design of FIR filters
7. 10.6 Further Reading
8. MATLAB Exercises
9. Problems
10. MATLAB Problems
11. MATLAB Projects
14. Chapter 11 Amplitude Modulation
1. Chapter Objectives
2. 11.1 Introduction
3. 11.2 The Need for Modulation
4. 11.3 Types of Modulation
5. 11.4 Amplitude Modulation
1. 11.4.1 Frequency spectrum of the AM signal
2. 11.4.2 Power balance and modulation efficiency
3. 11.4.3 Generation of AM signals
4. 11.4.4 Demodulation of AM signals
6. 11.5 Double-Sideband Suppressed Carrier Modulation
7. 11.6 Single-Sideband Modulation
8. 11.7 Further Reading
9. MATLAB Exercises
10. Problems
11. MATLAB Problems
12. MATLAB Projects
15. Appendix A Complex Numbers and Euler’s Formula
1. A.1 Introduction
2. A.2 Arithmetic with Complex Numbers
3. A.3 Euler’s Formula
16. Appendix B Mathematical Relations
17. Appendix C Closed Forms for Sums of Geometric Series
18. Appendix D Orthogonality of Basis Functions
19. Appendix E Partial Fraction Expansion
20. Appendix F Review of Matrix Algebra

## Product information

• Title: Signals and Systems
• Author(s): Oktay Alkin
• Release date:
• Publisher(s): CRC Press
• ISBN: None