## Book Description

Practical Signals Theory with MATLAB Applications is organized around applications, first introducing the actual behavior of specific signals and then using them to motivate the presentation of mathematical concepts. Tervo sequences the presentation of the major transforms by their complexity: first Fourier, then Laplace, and finally the z-transform.

The goal is to help students who can't visualize phenomena from an equation to develop their intuition and learn to analyze signals by inspection.

Finally, most examples and problems are designed to use MATLAB, making the presentation more in line with modern engineering practice.

1. Coverpage
2. Titlepage
4. Dedication
5. Brief Contents
6. Contents
7. Preface
8. Acknowledgments
9. 1 Introduction to Signals and Systems
1. 1.1 Introduction
2. 1.2 Introduction to Signal Manipulation
1. 1.2.1 Linear Combination
2. 1.2.2 Addition and Multiplication of Signals
3. 1.2.3 Visualizing Signals—An Important Skill
4. 1.2.4 Introduction to Signal Manipulation Using MATLAB
3. 1.3 A Few Useful Signals
1. 1.3.1 The Unit Rectangle rect(t)
2. 1.3.2 The Unit Step u(t)
3. 1.3.3 Reflection about t = 0
4. 1.3.4 The Exponential ext
5. 1.3.5 The Unit Impulse δ(t)
4. 1.4 The Sinusoidal Signal
5. 1.5 Phase Change vs. Time Shift
6. 1.6 Useful Hints and Help with MATLAB
7. 1.7 Conclusions
10. 2 Classification of Signals
1. 2.1 Introduction
2. 2.2 Periodic Signals
3. 2.3 Odd and Even Signals
1. 2.3.1 Combining Odd and Even Signals
2. 2.3.2 The Constant Value s(t) = A
3. 2.3.3 Trigonometric Identities
4. 2.3.4 The Modulation Property
4. 2.4 Energy and Power Signals
1. 2.4.1 Periodic Signals = Power Signals
2. 2.4.2 Comparing Signal Power: The Decibel (dB)
5. 2.5 Complex Signals
6. 2.6 Discrete Time Signals
7. 2.7 Digital Signals
8. 2.8 Random Signals
9. 2.9 Useful Hints and Help with MATLAB
10. 2.10 Conclusions
11. 3 Linear Systems
1. 3.1 Introduction
2. 3.2 Definition of a Linear System
1. 3.2.1 Superposition
2. 3.2.2 Linear System Exercise 1: Zero State Response
3. 3.2.3 Linear System Exercise 2: Operating in a Linear Region
4. 3.2.4 Linear System Exercise 3: Mixer
5. 3.2.5 Linear Time-Invariant (LTI) Systems
6. 3.2.6 Bounded Input, Bounded Output
7. 3.2.7 System Behavior as a Black Box
3. 3.3 Linear System Response Function h(t)
4. 3.4 Convolution
1. 3.4.1 The Convolution Integral
2. 3.4.2 Convolution Is Commutative
3. 3.4.3 Convolution Is Associative
4. 3.4.4 Convolution Is Distributive over Addition
5. 3.4.5 Evaluation of the Convolution Integral
6. 3.4.6 Convolution Properties
7. 3.4.7 Convolution with MATLAB
5. 3.5 Determining h(t) in an Unknown System
1. 3.5.1 The Unit Impulse δ(t)Test Signal
2. 3.5.2 Convolution and Signal Decomposition
3. 3.5.3 An Ideal Distortionless System
6. 3.6 Causality
7. 3.7 Combined Systems
8. 3.8 Convolution and Random Numbers
9. 3.9 Useful Hints and Help with MATLAB
10. 3.10 Chapter Summary
11. 3.11 Conclusions
12. 4 The Fourier Series
1. Chapter Overview
2. 4.1 Introduction
3. 4.2 Expressing Signals by Components
4. 4.3 Part One—Orthogonal Signals
5. 4.4 Orthogonality
1. 4.4.1 An Orthogonal Signal Space
2. 4.4.2 The Signal Inner Product Formulation
3. 4.4.3 Complete Set of Orthogonal Signals
4. 4.4.4 What If a Complete Set Is Not Present?
5. 4.4.5 An Orthogonal Set of Signals
6. 4.4.6 Orthogonal Signals and Linearly Independent Equations
6. 4.5 Part Two—The Fourier Series
7. 4.6 Computing Fourier Series Components
8. 4.7 Fundamental Frequency Component
9. 4.8 Practical Harmonics
10. 4.9 Odd and Even Square Waves
11. 4.10 Gibb’s Phenomenon
12. 4.11 Setting Up the Fourier Series Calculation
1. 4.11.1 Appearance of Pulse Train Frequency Components
13. 4.12 Some Common Fourier Series
14. 4.13 Part Three—The Complex Fourier Series
15. 4.14 The Complex Fourier Series
16. 4.15 Complex Fourier Series Components
17. 4.16 Properties of the Complex Fourier Series
18. 4.17 Analysis of a DC Power Supply
19. 4.18 The Fourier Series with MATLAB
1. 4.18.1 Essential Features of the fft() in MATLAB
2. 4.18.2 Full-Wave Rectified Cosine (60 Hz)
3. 4.18.3 Useful Hints and Help with MATLAB
20. 4.19 Conclusions
13. 5 The Fourier Transform
1. 5.1 Introduction
2. 5.2 Properties of the Fourier Transform
3. 5.3 The Rectangle Signal
4. 5.4 The Sinc Function
5. 5.5 Signal Manipulations: Time and Frequency
6. 5.6 Fourier Transform Pairs
7. 5.7 Rapid Changes vs. High Frequencies
8. 5.8 Conclusions
14. 6 Practical Fourier Transforms
1. 6.1 Introduction
2. 6.2 Convolution: Time and Frequency
3. 6.3 Transfer Function of a Linear System
4. 6.4 Energy in Signals: Parseval’s Theorem for the Fourier Transform
5. 6.5 Data Smoothing and the Frequency Domain
6. 6.6 Ideal Filters
7. 6.7 A Real Lowpass Filter
8. 6.8 The Modulation Theorem
1. 6.8.1 A Voice Privacy System
9. 6.9 Periodic Signals and the Fourier Transform
1. 6.9.1 The Impulse Train
2. 6.9.2 General Appearance of Periodic Signals
3. 6.9.3 The Fourier Transform of a Square Wave
4. 6.9.4 Other Periodic Waveforms
10. 6.10 The Analog Spectrum Analyzer
11. 6.11 Conclusions
15. 7 The Laplace Transform
1. 7.1 Introduction
2. 7.2 The Laplace Transform
3. 7.3 Exploring the s-Domain
1. 7.3.1 A Pole at the Origin
2. 7.3.2 Decaying Exponential
3. 7.3.3 A Sinusoid
4. 7.3.4 A Decaying Sinusoid
5. 7.3.5 An Unstable System
4. 7.4 Visualizing the Laplace Transform
1. 7.4.1 First-Order Lowpass Filter
2. 7.4.2 Pole Position Determines Frequency Response
3. 7.4.3 Second-Order Lowpass Filter
4. 7.4.4 Two-Sided Laplace Transform
5. 7.4.5 The Bode Plot
6. 7.4.6 System Analysis in MATLAB
5. 7.5 Properties of the Laplace Transform
6. 7.6 Differential Equations
1. 7.6.1 Solving a Differential Equation
2. 7.6.2 Transfer Function as Differential Equations
7. 7.7 Laplace Transform Pairs
8. 7.8 Circuit Analysis with the Laplace Transform
1. 7.8.1 Voltage Divider
2. 7.8.2 A First-Order Lowpass Filter
3. 7.8.3 A First-Order Highpass Filter
4. 7.8.4 A Second-Order Filter
9. 7.9 State Variable Analysis
10. 7.10 Conclusions
16. 8 Discrete Signals
1. 8.1 Introduction
2. 8.2 Discrete Time vs. Continuous Time Signals
3. 8.3 A Discrete Time Signal
4. 8.4 Data Collection and Sampling Rate
5. 8.5 Introduction to Digital Filtering
6. 8.6 Illustrative Examples
1. MATLAB Exercise 1: The FFT and the Inverse FFT
2. 8.6.1 FFT and Sample Rate
3. 8.6.2 Practical DFT Issues
7. 8.7 Discrete Time Filtering with MATLAB
8. 8.8 Conclusions
17. 9 The z-Transform
1. 9.1 Introduction
2. 9.2 The z-Transform
3. 9.3 Calculating the z-Transform
4. 9.4 A Discrete Time Laplace Transform
5. 9.5 Properties of the z-Transform
6. 9.6 z-Transform Pairs
7. 9.7 Transfer Function of a Discrete Linear System
8. 9.8 MATLAB Analysis with the z-Transform
9. 9.9 Digital Filtering—FIR Filter
1. 9.9.1 A One-Pole FIR Filter
2. 9.9.2 A Two-Pole FIR Filter
3. 9.9.3 Higher-Order FIR Filters
10. 9.10 Digital Filtering—IIR Filter
11. 9.11 Conclusions
18. 10 Introduction to Communications
1. 10.1 Introduction
2. 10.2 Amplitude Modulation
3. 10.3 Suppressed Carrier Transmission
5. 10.5 Digital Communications
6. 10.6 Phase Shift Keying
7. 10.7 Conclusions
19. A The Illustrated Fourier Transform
20. B The Illustrated Laplace Transform
21. C The Illustrated z-Transform
22. D MATLAB Reference Guide
1. D.1 Defining Signals
2. D.2 Complex Numbers
3. D.3 Plot Commands
4. D.4 Signal Operations
5. D.5 Defining Systems
1. D.5.1 System Definition
2. D.5.2 System Analysis
6. D.6 Example System Definition and Test
23. E Reference Tables
1. E.1 Fourier Transform
2. E.2 Laplace Transform
3. E.3 z-Transform
24. Bibliography
25. Index

## Product Information

• Title: Practical Signals Theory with MATLAB Applications
• Author(s): Richard J. Tervo
• Release date: February 2013
• Publisher(s): Wiley
• ISBN: 9781118115398