i “book” — 2012/2/28 — 2:59 — page ix — #9i Contents Preface Chapter 1 Signals 1-1 1-2 1-3 1-4 1-5 Overview Types of Signals Signal Transformations Waveform Properties Nonperiodic Waveforms Signal Power and Energy Chapter 1 Summary Problems xiii 1 2 3 6 9 11 21 24 25 Chapter 3 Laplace Transform 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10 3-11 Overview Definition of the (Unilateral) Laplace Transform Poles and Zeros Properties of the Laplace Transform Circuit Analysis Example Partial Fraction Expansion Transfer Function H(s) Poles and System Stability Invertible Systems Bilateral Transform for Continuous-Time Sinusoidal Signals Interrelating Different Descriptions of LTI Systems LTI System Response Partitions Chapter 3 Summary Problems 83 84 84 87 88 96 97 104 106 109 111 112 115 121 122 Chapter 2 Linear Time-Invariant Systems 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 Overview Linear Time-Invariant Systems Impulse Response Convolution Graphical Convolution Convolution Properties Causality and BIBO Stability LTI Sinusoidal Response Impulse Response of Second-Order LCCDEs Car Suspension System Chapter 2 Summary Problems 30 31 31 35 40 46 49 57 60 64 71 77 78 Chapter 4 Applications of the Laplace Transform 4-1 4-2 4-3 4-4 Overview s-Domain Circuit Element Models s-Domain Circuit Analysis Electromechanical Analogs Biomechanical Model of a Person Sitting in a Moving Chair 128 129 129 131 137 143 i i Fourier Circuit Analysis with Fourier Transform The Importance of Phase Information Chapter 5 Summary Problems 187 188 188 190 192 193 207 210 212 217 224 225 228 229 230 236 237 Chapter 7 Discrete-Time Signals and 331 Systems Overview 7-1 7-2 7-3 7-4 7-5 7-6 7-7 7-8 7-9 7-10 7-11 7-12 7-13 7-14 7-15 7-16 Discrete Signal Notation and Properties Discrete-Time Signal Functions Discrete-Time LTI Systems Properties of Discrete-Time LTI Systems Discrete-Time Convolution The z-Transform Properties of the z-Transform Inverse z-Transform Solving Difference Equations with Initial Conditions System Transfer Function BIBO Stability of H(z) System Frequency Response Discrete-Time Fourier Series (DTFS) Discrete-Time Fourier Transform (DTFT) Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT) Chapter 7 Summary Problems 332 333 336 341 344 348 350 354 359 362 364 365 367 372 377 383 387 390 391 Chapter 6 Applications of the Fourier Transform Overview 6-1 6-2 6-3 6-4 Signal Filtering Passive Filters Active Filters Ideal Brick-Wall Filters 245 246 246 254 262 266 Chapter 8 Applications of 396 Discrete-Time Signals and Systems Overview 8-1 8-2 8-3 Discrete-Time Filters Notch Filters Comb Filters 397 397 402 407 i i .i “book” — 2012/2/28 — 2:59 — page x — #10 i x 4-5 4-6 4-7 4-8 4-9 4-10 4-11 4-12 Op-Amp Circuits Configurations of Multiple Systems System Synthesis Basic Control Theory Temperature Control System Amplifier Gain-Bandwidth Product Step Response of a Motor System Control of a Simple Inverted Pendulum on a Cart Chapter 4 Summary Problems 146 151 154 157 164 168 170 173 178 179 6-5 6-6 6-7 6-8 6-9 6-10 6-11 6-12 Filter Design by Poles and Zeros Frequency Rejection Filters Spectra of Musical Notes Butterworth Filters De-Noising a Trumpet Signal Resonator Filter Amplitude Modulation Sampling Theorem Chapter 6 Summary Problems 268 272 278 279 287 290 292 306 321 323 Chapter 5 Fourier Analysis Techniques Overview 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9 5-10 5-11 5-12 5-13 Phasor-Domain Technique Fourier Series Analysis Technique Fourier Series Representations Computation of Fourier Series Coefficients Circuit Analysis with Fourier Series Parseval’s Theorem for Periodic Waveforms Fourier Transform Fourier Transform Properties Parseval’s Theorem for Fourier Transforms Additional Attributes of the Fourier Transform Phasor vs. Laplace vs. i “book” — 2012/2/28 — 2:59 — page xi — #11 i xi 8-4 8-5 8-6 8-7 Deconvolution and Dereverberation Deconvolution and Filtering Using the DFT Computing Spectra of Periodic Signals Computing Spectra of Nonperiodic Signals Chapter 8 Summary Problems 411 417 422 426 432 433 Appendix C Mathematical Formulas Appendix D MATLAB® and NI LabVIEW MathScript RT Module Appendix E Answers to Selected Problems Index 443 446 454 Appendix A Symbols. Quantities. and 437 Units Appendix B Review of Complex Numbers 439 457 i i .