A Practical Approach to Signals and SystemsISBN: 9780470823538
400 pages
August 2008

Description
Gaining a strong sense of signals and systems fundamentals is key for general proficiency in any electronic engineering discipline, and critical for specialists in signal processing, communication, and control. At the same time, there is a pressing need to gain mastery of these concepts quickly, and in a manner that will be immediately applicable in the real word.
Simultaneous study of both continuous and discrete signals and systems presents a much easy path to understanding signals and systems analysis. In A Practical Approach to Signals and Systems, Sundararajan details the discrete version first followed by the corresponding continuous version for each topic, as discrete signals and systems are more often used in practice and their concepts are relatively easier to understand. In addition to examples of typical applications of analysis methods, the author gives comprehensive coverage of transform methods, emphasizing practical methods of analysis and physical interpretations of concepts.

Gives equal emphasis to theory and practice

Presents methods that can be immediately applied

Complete treatment of transform methods

Expanded coverage of Fourier analysis

Selfcontained: starts from the basics and discusses applications

Visual aids and examples makes the subject easier to understand

Endofchapter exercises, with a extensive solutions manual for instructors

MATLAB software for readers to download and practice on their own

Presentation slides with book figures and slides with lecture notes
A Practical Approach to Signals and Systems is an excellent resource for the electrical engineering student or professional to quickly gain an understanding of signal analysis concepts  concepts which all electrical engineers will eventually encounter no matter what their specialization. For aspiring engineers in signal processing, communication, and control, the topics presented will form a sound foundation to their future study, while allowing them to quickly move on to more advanced topics in the area.
Scientists in chemical, mechanical, and biomedical areas will also benefit from this book, as increasing overlap with electrical engineering solutions and applications will require a working understanding of signals. Compact and self contained, A Practical Approach to Signals and Systems be used for courses or selfstudy, or as a reference book.
Table of Contents
Preface xiii
Abbreviations xv
1 Introduction 1
1.1 The Organization of this Book 1
2 Discrete Signals 5
2.1 Classification of Signals 5
2.1.1 Continuous, Discrete and Digital Signals 5
2.1.2 Periodic and Aperiodic Signals 7
2.1.3 Energy and Power Signals 7
2.1.4 Even and Oddsymmetric Signals 8
2.1.5 Causal and Noncausal Signals 10
2.1.6 Deterministic and Random Signals 10
2.2 Basic Signals 11
2.2.1 Unitimpulse Signal 11
2.2.2 Unitstep Signal 12
2.2.3 Unitramp Signal 13
2.2.4 Sinusoids and Exponentials 13
2.3 Signal Operations 20
2.3.1 Time Shifting 21
2.3.2 Time Reversal 21
2.3.3 Time Scaling 22
2.4 Summary 23
Further Reading 23
Exercises 23
3 Continuous Signals 29
3.1 Classification of Signals 29
3.1.1 Continuous Signals 29
3.1.2 Periodic and Aperiodic Signals 30
3.1.3 Energy and Power Signals 31
3.1.4 Even and Oddsymmetric Signals 31
3.1.5 Causal and Noncausal Signals 33
3.2 Basic Signals 33
3.2.1 Unitstep Signal 33
3.2.2 Unitimpulse Signal 34
3.2.3 Unitramp Signal 42
3.2.4 Sinusoids 43
3.3 Signal Operations 45
3.3.1 Time Shifting 45
3.3.2 Time Reversal 46
3.3.3 Time Scaling 47
3.4 Summary 48
Further Reading 48
Exercises 48
4 Timedomain Analysis of Discrete Systems 53
4.1 Difference Equation Model 53
4.1.1 System Response 55
4.1.2 Impulse Response 58
4.1.3 Characterization of Systems by their Responses to Impulse and Unitstep Signals 60
4.2 Classification of Systems 61
4.2.1 Linear and Nonlinear Systems 61
4.2.2 Timeinvariant and Timevarying Systems 62
4.2.3 Causal and Noncausal Systems 63
4.2.4 Instantaneous and Dynamic Systems 64
4.2.5 Inverse Systems 64
4.2.6 Continuous and Discrete Systems 64
4.3 Convolution–Summation Model 64
4.3.1 Properties of Convolution–Summation 67
4.3.2 The Difference Equation and Convolution–Summation 68
4.3.3 Response to Complex Exponential Input 69
4.4 System Stability 71
4.5 Realization of Discrete Systems 72
4.5.1 Decomposition of Higherorder Systems 73
4.5.2 Feedback Systems 74
4.6 Summary 74
Further Reading 75
Exercises 75
5 Timedomain Analysis of Continuous Systems 79
5.1 Classification of Systems 80
5.1.1 Linear and Nonlinear Systems 80
5.1.2 Timeinvariant and Timevarying Systems 81
5.1.3 Causal and Noncausal Systems 82
5.1.4 Instantaneous and Dynamic Systems 83
5.1.5 Lumpedparameter and Distributedparameter Systems 83
5.1.6 Inverse Systems 83
5.2 Differential Equation Model 83
5.3 Convolutionintegral Model 85
5.3.1 Properties of the Convolutionintegral 87
5.4 System Response 88
5.4.1 Impulse Response 88
5.4.2 Response to Unitstep Input 89
5.4.3 Characterization of Systems by their Responses to Impulse and Unitstep Signals 91
5.4.4 Response to Complex Exponential Input 92
5.5 System Stability 93
5.6 Realization of Continuous Systems 94
5.6.1 Decomposition of Higherorder Systems 94
5.6.2 Feedback Systems 95
5.7 Summary 96
Further Reading 97
Exercises 97
6 The Discrete Fourier Transform 101
6.1 The Timedomain and the Frequencydomain 101
6.2 Fourier Analysis 102
6.2.1 Versions of Fourier Analysis 104
6.3 The Discrete Fourier Transform 104
6.3.1 The Approximation of Arbitrary Waveforms with a Finite Number of Samples 104
6.3.2 The DFT and the IDFT 105
6.3.3 DFT of Some Basic Signals 107
6.4 Properties of the Discrete Fourier Transform 110
6.4.1 Linearity 110
6.4.2 Periodicity 110
6.4.3 Circular Shift of a Sequence 110
6.4.4 Circular Shift of a Spectrum 111
6.4.5 Symmetry 111
6.4.6 Circular Convolution of Timedomain Sequences 112
6.4.7 Circular Convolution of Frequencydomain Sequences 113
6.4.8 Parseval’s Theorem 114
6.5 Applications of the Discrete Fourier Transform 114
6.5.1 Computation of the Linear Convolution Using the DFT 114
6.5.2 Interpolation and Decimation 115
6.6 Summary 119
Further Reading 119
Exercises 119
7 Fourier Series 123
7.1 Fourier Series 123
7.1.1 FS as the Limiting Case of the DFT 123
7.1.2 The Compact Trigonometric Form of the FS 125
7.1.3 The Trigonometric Form of the FS 126
7.1.4 Periodicity of the FS 126
7.1.5 Existence of the FS 126
7.1.6 Gibbs Phenomenon 130
7.2 Properties of the Fourier Series 132
7.2.1 Linearity 133
7.2.2 Symmetry 133
7.2.3 Time Shifting 135
7.2.4 Frequency Shifting 135
7.2.5 Convolution in the Timedomain 136
7.2.6 Convolution in the Frequencydomain 137
7.2.7 Duality 138
7.2.8 Time Scaling 138
7.2.9 Time Differentiation 139
7.2.10 Time Integration 140
7.2.11 Parseval’s Theorem 140
7.3 Approximation of the Fourier Series 141
7.3.1 Aliasing Effect 142
7.4 Applications of the Fourier Series 144
7.5 Summary 145
Further Reading 145
Exercises 145
8 The Discretetime Fourier Transform 151
8.1 The Discretetime Fourier Transform 151
8.1.1 The DTFT as the Limiting Case of the DFT 151
8.1.2 The Dual Relationship Between the DTFT and the FS 156
8.1.3 The DTFT of a Discrete Periodic Signal 158
8.1.4 Determination of the DFT from the DTFT 158
8.2 Properties of the Discretetime Fourier Transform 159
8.2.1 Linearity 159
8.2.2 Time Shifting 159
8.2.3 Frequency Shifting 160
8.2.4 Convolution in the Timedomain 161
8.2.5 Convolution in the Frequencydomain 162
8.2.6 Symmetry 163
8.2.7 Time Reversal 164
8.2.8 Time Expansion 164
8.2.9 Frequencydifferentiation 166
8.2.10 Difference 166
8.2.11 Summation 167
8.2.12 Parseval’s Theorem and the Energy Transfer Function 168
8.3 Approximation of the Discretetime Fourier Transform 168
8.3.1 Approximation of the Inverse DTFT by the IDFT 170
8.4 Applications of the Discretetime Fourier Transform 171
8.4.1 Transfer Function and the System Response 171
8.4.2 Digital Filter Design Using DTFT 174
8.4.3 Digital Differentiator 174
8.4.4 Hilbert Transform 175
8.5 Summary 178
Further Reading 178
Exercises 178
9 The Fourier Transform 183
9.1 The Fourier Transform 183
9.1.1 The FT as a Limiting Case of the DTFT 183
9.1.2 Existence of the FT 185
9.2 Properties of the Fourier Transform 190
9.2.1 Linearity 190
9.2.2 Duality 190
9.2.3 Symmetry 191
9.2.4 Time Shifting 192
9.2.5 Frequency Shifting 192
9.2.6 Convolution in the Timedomain 193
9.2.7 Convolution in the Frequencydomain 194
9.2.8 Conjugation 194
9.2.9 Time Reversal 194
9.2.10 Time Scaling 194
9.2.11 Timedifferentiation 195
9.2.12 Timeintegration 197
9.2.13 Frequencydifferentiation 198
9.2.14 Parseval’s Theorem and the Energy Transfer Function 198
9.3 Fourier Transform of Mixed Classes of Signals 200
9.3.1 The FT of a Continuous Periodic Signal 200
9.3.2 Determination of the FS from the FT 202
9.3.3 The FT of a Sampled Signal and the Aliasing Effect 203
9.3.4 The FT of a Sampled Aperiodic Signal and the DTFT 206
9.3.5 The FT of a Sampled Periodic Signal and the DFT 207
9.3.6 Approximation of a Continuous Signal from its Sampled Version 209
9.4 Approximation of the Fourier Transform 209
9.5 Applications of the Fourier Transform 211
9.5.1 Transfer Function and System Response 211
9.5.2 Ideal Filters and their Unrealizability 214
9.5.3 Modulation and Demodulation 215
9.6 Summary 219
Further Reading 219
Exercises 219
10 The zTransform 227
10.1 Fourier Analysis and the zTransform 227
10.2 The zTransform 228
10.3 Properties of the zTransform 232
10.3.1 Linearity 232
10.3.2 Left Shift of a Sequence 233
10.3.3 Right Shift of a sequence 234
10.3.4 Convolution 234
10.3.5 Multiplication by n 235
10.3.6 Multiplication by an 235
10.3.7 Summation 236
10.3.8 Initial Value 236
10.3.9 Final Value 237
10.3.10 Transform of Semiperiodic Functions 237
10.4 The Inverse zTransform 237
10.4.1 Finding the Inverse zTransform 238
10.5 Applications of the zTransform 243
10.5.1 Transfer Function and System Response 243
10.5.2 Characterization of a System by its Poles and Zeros 245
10.5.3 System Stability 247
10.5.4 Realization of Systems 248
10.5.5 Feedback Systems 251
10.6 Summary 253
Further Reading 253
Exercises 253
11 The Laplace Transform 259
11.1 The Laplace Transform 259
11.1.1 Relationship Between the Laplace Transform and the zTransform 262
11.2 Properties of the Laplace Transform 263
11.2.1 Linearity 263
11.2.2 Time Shifting 264
11.2.3 Frequency Shifting 264
11.2.4 Timedifferentiation 265
11.2.5 Integration 267
11.2.6 Time Scaling 268
11.2.7 Convolution in Time 268
11.2.8 Multiplication by t 269
11.2.9 Initial Value 269
11.2.10 Final Value 270
11.2.11 Transform of Semiperiodic Functions 270
11.3 The Inverse Laplace Transform 271
11.4 Applications of the Laplace Transform 272
11.4.1 Transfer Function and System Response 272
11.4.2 Characterization of a System by its Poles and Zeros 273
11.4.3 System Stability 274
11.4.4 Realization of Systems 276
11.4.5 Frequencydomain Representation of Circuits 276
11.4.6 Feedback Systems 279
11.4.7 Analog Filters 282
11.5 Summary 285
Further Reading 285
Exercises 285
12 Statespace Analysis of Discrete Systems 293
12.1 The Statespace Model 293
12.1.1 Parallel Realization 297
12.1.2 Cascade Realization 299
12.2 Timedomain Solution of the State Equation 300
12.2.1 Iterative Solution 300
12.2.2 Closedform Solution 301
12.2.3 The Impulse Response 307
12.3 Frequencydomain Solution of the State Equation 308
12.4 Linear Transformation of State Vectors 310
12.5 Summary 312
Further Reading 313
Exercises 313
13 Statespace Analysis of Continuous Systems 317
13.1 The Statespace Model 317
13.2 Timedomain Solution of the State Equation 322
13.3 Frequencydomain Solution of the State Equation 327
13.4 Linear Transformation of State Vectors 330
13.5 Summary 332
Further Reading 333
Exercises 333
Appendix A: Transform Pairs and Properties 337
Appendix B: Useful Mathematical Formulas 349
Answers to Selected Exercises 355
Index 377
Author Information
The Wiley Advantage

Gives equal emphasis to theory and practice

Presents methods that can be immediately applied

Complete treatment of transform methods, with expanded coverage of Fourier analysis

Starts from the basics and discusses applications, and is therefore selfcontained

Visual aids and examples makes the subject easier to understand

Endofchapter exercises, with a extensive solutions manual for instructors

MATLAB software for readers to download and practice on their own

Presentation slides with book figures and slides with lecture notes
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