Signals and Systems For Dummies

Getting mixed signals in your signals and systems course? The concepts covered in a typical signals and systems course are often considered by engineering students to be some of the most difficult to master. Thankfully, Signals & Systems For Dummies is your intuitive guide to this tricky course, walking you step-by-step through some of the more complex theories and mathematical formulas in a way that is easy to understand.

From Laplace Transforms to Fourier Analyses, Signals & Systems For Dummies explains in plain English the difficult concepts that can trip you up. Perfect as a study aid or to complement your classroom texts, this friendly, hands-on guide makes it easy to figure out the fundamentals of signal and system analysis.

• Serves as a useful tool for electrical and computer engineering students looking to grasp signal and system analysis
• Provides helpful explanations of complex concepts and techniques related to signals and systems
• Includes worked-through examples of real-world applications using Python, an open-source software tool, as well as a custom function module written for the book

• Brings you up-to-speed on the concepts and formulas you need to know
  Signals & Systems For Dummies is your ticket to scoring high in your introductory signals and systems course.

Auteur

Mark Wickert, PhD, is a Professor of Electrical and Computer Engineering at the University of Colorado, Colorado Springs. He is a member of the IEEE and is doing real signals and systems problem solving as a consultant with local industry.

Résumé
Getting mixed signals in your signals and systems course? The concepts covered in a typical signals and systems course are often considered by engineering students to be some of the most difficult to master. Thankfully, Signals & Systems For Dummies is your intuitive guide to this tricky course, walking you step-by-step through some of the more complex theories and mathematical formulas in a way that is easy to understand.

From Laplace Transforms to Fourier Analyses, Signals & Systems For Dummies explains in plain English the difficult concepts that can trip you up. Perfect as a study aid or to complement your classroom texts, this friendly, hands-on guide makes it easy to figure out the fundamentals of signal and system analysis.

• Serves as a useful tool for electrical and computer engineering students looking to grasp signal and system analysis
• Provides helpful explanations of complex concepts and techniques related to signals and systems
• Includes worked-through examples of real-world applications using Python, an open-source software tool, as well as a custom function module written for the book
• Brings you up-to-speed on the concepts and formulas you need to know
  Signals & Systems For Dummies is your ticket to scoring high in your introductory signals and systems course.

Contenu

Introduction 1

About This Book 1

Conventions Used in This Book 1

What You're Not to Read 2

Foolish Assumptions 2

How This Book Is Organized 2

Part I: Getting Started with Signals and Systems 3

Part II: Exploring the Time Domain 3

Part III: Picking Up the Frequency Domain 3

Part IV: Entering the s- and z-Domains 3

Part V: The Part of Tens 4

Icons Used in This Book 4

Where to Go from Here 4

Part I: Getting Started with Signals and Systems 7

Chapter 1: Introducing Signals and Systems 9

Applying Mathematics 10

Getting Mixed Signals and Systems 11

Going on and on and on 11

Working in spurts: Discrete-time signals and systems 13

Classifying Signals 14

Periodic 14

Aperiodic 15

Random 15

Signals and Systems in Other Domains 16

Viewing signals in the frequency domain 16

Traveling to the s- or z-domain and back 18

Testing Product Concepts with Behavioral Level Modeling 18

Staying abstract to generate ideas 19

Working from the top down 19

Relying on mathematics 20

Exploring Familiar Signals and Systems 20

MP3 music player 21

Smartphone 22

Automobile cruise control 22

Using Computer Tools for Modeling and Simulation 23

Getting the software 24

Exploring the interfaces 25

Seeing the Big Picture 26

Chapter 2: Brushing Up on Math 29

Revealing Unknowns with Algebra 29

Solving for two variables 30

Checking solutions with computer tools 30

Exploring partial fraction expansion 31

Making Nice Signal Models with Trig Functions 35

Manipulating Numbers: Essential Complex Arithmetic 36

Believing in imaginary numbers 37

Operating with the basics 39

Applying Euler's identities 41

Applying the phasor addition formula 42

Catching Up with Calculus 44

Differentiation 44

Integration 45

System performance 47

Geometric series 48

Finding Polynomial Roots 50

Chapter 3: Continuous-Time Signals and Systems 51

Considering Signal Types 52

Exponential and sinusoidal signals 52

Singularity and other special signal types 55

Getting Hip to Signal Classifications 60

Deterministic and random 60

Periodic and aperiodic 62

Considering power and energy 63

Even and odd signals 68

Transforming Simple Signals 69

Time shifting 69

Flipping the time axis 70

Putting it together: Shift and flip 70

Superimposing signals 71

Checking Out System Properties 72

Linear and nonlinear 73

Time-invariant and time varying 73

Causal and non-causal 74

Memory and memoryless 74

Bounded-input bounded-output 75

Choosing Linear and Time-Invariant Systems 75

Chapter 4: Discrete-Time Signals and Systems 77

Exploring Signal Types 77

Exponential and sinusoidal signals 78

Special signals 80

Surveying Signal Classifications in the Discrete-Time World 83

Deterministic and random signals 84

Periodic and aperiodic 85

Recognizing energy and power signals 88

Computer Processing: Capturing Real Signals in Discrete-Time 89

Capturing and reading a wav file 90

Finding the signal energy 91

Classifying Systems in Discrete-Time 92

Checking linearity 92

Investigating time invariance 93

Looking into causality 93

Figuring out memory 94

Testing for BIBO stability 95

Part II: Exploring the Time Domain 97

Chapter 5: Continuous-Time LTI Systems and the Convolution Integral 99

Establishing a General Input/Output Relationship 100

LTI systems and the impulse response 100

Developing the convolution integral 101

Looking at useful convolution integral properties 103

Working with the Convolution Integral 105

Seeing the general solution first 105

Solving problems with finite extent signals 107

Dealing with semi-infinite limits 111

Stepping Out and More 116

Step response from impulse response 116

BIBO stability implications 117

Causality and the impulse response 117

Chapter 6: Discrete-Time LTI Systems and the Convolution Sum 119

Specializing the Input/Output Relationship 120

Using LTI systems and the impulse response (sequence) 120

Getting to the convolution sum 121

Simplifying with Convolution Sum Properties and Techniques 124

Applying commutative, associative, and distributive properties 124

Convolving with the impulse function 126

Transforming a sequence 126

Solving convolution of finite duration sequences 128

Working with the Convolution Sum 133

Using spreadsheets and a tabular approach 133

Attacking the sum directly with geometric series 136

Connecting the step response and impulse response 144

Checking the BIBO stability 145

Checking for system causality 146

Chapter 7: LTI System Differential and Difference Equations in the Time Domain 149

Getting Differential 150

Introducing the general Nth-order system 150

Considering sinusoidal outputs in steady state 151

Finding the frequency response in general Nth-order LCC differential equ…