Signals, systems, and transforms

For sophomore/junior-level signals and systems courses in Electrical and Computer Engineering departments. This text provides a clear, comprehensive presentation of both the theory and applications in signals, systems, and transforms. It presents the mathematical background of signals and systems, including the Fourier transform, the Fourier series, the Laplace transform, the discrete-time and the discrete Fourier transforms, and the z-transform. The text integrates MATLAB examples into the presentation of signal and system theory and applications. INDICE: Preface xvii 1 Introduction 1 1.1 Modeling 1 1.2 Continuous-Time Physical Systems 4 Electric Circuits, 4 Operational Amplifier Circuits, 6 Simple Pendulum, 9 DC Power Supplies, 10 Analogous Systems, 12 1.3 Samplers and Discrete-Time Physical Systems 14 Analog-to-Digital Converter, 14 Numerical Integration, 16 Picture in a Picture, 17 Compact Disks, 18 Sampling in Telephone Systems, 19 Data-Acquisition System, 21 1.4 Matlab and Simulink 22 2 Continuous-Time Signals and Systems 24 2.1 Transformations of Continuous-Time Signals 25 Time Transformations, 25 Amplitude Transformations, 31 2.2 Signal Characteristics 33 Even and Odd Signals, 33 Periodic Signals, 35 2.3 Common Signals in Engineering 40 2.4 Singularity Functions 46 Unit Step Function, 46 Unit Impulse Function, 50 2.5 Mathematical Functions for Signals 55 2.6 Continuous-Time Systems 60 Interconnecting Systems, 62 Feedback System, 64 2.7 Properties of Continuous-Time Systems 66 Stability 70 Linearity 75 Summary 77 Problems 79 3 Continuous-Time Linear Time-Invariant Systems 89 3.1 Impulse Representation of Continuous-Time Signals 90 3.2 Convolution for Continuous-Time LTI Systems 93 3.3 Properties of Convolution 105 3.4 Properties of Continuous-Time LTI Systems 109 Memoryless Systems, 110 Invertibility, 110 Causality, 111 Stability, 112 Unit Step Response, 113 3.5 Differential-Equation Models 114 Solution of Differential Equations, 116 General Case, 118 Relation to Physical Systems, 120 3.6 Terms in the Natural Response 121 Stability, 122 3.7 System Response for Complex-Exponential Inputs 125 Linearity, 125 Complex Inputs for LTI Systems, 126 Impulse Response, 130 3.8 Block Diagrams 131 Direct Form I, 135 Direct Form II, 135 nth-Order Realizations, 135 Practical Considerations, 137 Summary 139 Problems 141 4 Fourier Series 152 4.1 Approximating Periodic Functions 153 PeriodicFunctions, 153 Approximating Periodic Functions, 154 4.2 Fourier Series 158 Fourier Series, 159 Fourier Coefficients, 160 4.3 Fourier Series and Frequency Spectra 163 Frequency Spectra, 164 4.4 Properties of Fourier Series 173 4.5 System Analysis 176 4.6 Fourier Series Transformations 183 Amplitude Transformations, 184 Time Transformations, 186 Summary 188 Problems 189 5 The Fourier Transform 199 5.1 Definition of the Fourier Transform 199 5.2 Properties of the Fourier Transform 208 Linearity, 208 Time Scaling, 210 Time Shifting, 213 Time Transformation, 214 Duality, 215 Convolution, 218 Frequency Shifting, 219 TimeDifferentiation, 221 Time Integration, 226 Frequency Differentiation, 229 Summary, 229 5.3 Fourier Transforms of Time Functions 230 DC Level, 230 Unit StepFunction, 230 Switched Cosine, 231 Pulsed Cosine, 231 Exponential Pulse, 233 Fourier Transforms of Periodic Functions, 233 Summary, 239 5.4 Sampling Continuous-Time Signals 239 Impulse Sampling, 240 Shannon's Sampling Theorem, 242 Practical Sampling, 244 5.5 Application of the Fourier Transform 244 Frequency Response of Linear Systems, 244 Frequency Spectra of Signals, 253 Summary, 256 5.6 Energy and Power Density Spectra 256 Energy Density Spectrum, 256 Power Density Spectrum, 259 Power and Energy Transmission, 262 Summary, 264 Summary 265 Problems 267 6 Applications of the Fourier Transform 275 6.1 Ideal Filters 275 6.2 Real Filters 282 RC Low-Pass Filter, 283 Butterworth Filter, 285 Chebyschev and Elliptic Filters, 291 Bandpass Filters, 295 Summary, 296 6.3 Bandwidth Relationships 296 6.4 Reconstruction of signals from sample data 300 Interpolating Function, 302 Digital-to-analog Conversion, 304 6.5 Sinusoidal Amplitude Modulation 307 Frequency-Division Multiplexing, 316 6.6 Pulse-Amplitude Modulation 318 Time-Division Multiplexing, 320 Flat-Top PAM, 322 Summary 325 Problems 326 7 The Laplace Transform 337 7.1 Definitions of Laplace Transforms 338 7.2 Examples 341 7.3 Laplace Transforms of Functions 346 7.4 Laplace TransformProperties 350 Real Shifting, 351 Differentiation, 355 Integration, 357 7.5 Additional Properties 358 Multiplication by t, 358 Initial Value, 359 Final Value, 360 Time Transformation, 361 7.6 Response of LTI Systems 364 Initial Conditions, 364 Transfer Functions, 365 Convolution, 370 Transforms with Complex Poles, 372 Functions with Repeated Poles, 375 7.7 LTI Systems Characteristics 376 Causality, 376 Stability, 377 Invertibility, 379 Frequency Response, 380 7.8Bilateral Laplace Transform 382 Region of Convergence, 384 Bilateral Transform from Unilateral Tables, 386 Inverse Bilateral Laplace Transform, 388 7.9 Relationship of the Laplace Transform to the Fourier Transform 390 Summary 391 Problems 392 8 State Variables for Continuous-Time Systems 400 8.1 State-Variable Modeling 401 8.2 Simulation Diagrams 405 8.3 Solution of State Equations 410Laplace-Transform Solution, 411 Convolution Solution, 416 Infinite Series Solution, 417 8.4 Properties of the State Transition Matrix 420 8.5 Transfer Functions 422 Stability, 424 8.6 Similarity Transformations 426 Transformations, 426 Properties, 432 Summary 434 Problems 436 9 Discrete-Time Signals and Systems 445 9.1 Discrete-Time Signals and Systems 447 Unit Step and Unit Impulse Functions, 449 Equivalent Operations, 451 9.2 Transformations of Discrete-Time Signals 452 Time Transformations, 453 Amplitude Transformations, 458 9.3 Characteristics of Discrete-Time Signals 461 Even and Odd Signals, 461 Signals Periodic in n, 464 Signals Periodic in W 467 9.4 Common Discrete-Time Signals 468 9.5 Discrete-Time Systems 474 Interconnecting Systems, 475 9.6 Properties of Discrete-Time Systems 477 Systems with Memory, 477 Invertibility, 478 Inverse of a System, 479 Causality, 479 Stability, 480 Time Invariance, 480 Linearity, 481 Summary 483 Problems 485 10 Discrete-Time Linear Time-Invariant Systems 493 10.1 Impulse Representation of Discrete-Time Signals 494 10.2 Convolution for Discrete-Time Systems 495 Properties of Convolution, 504 10.3 Properties of Discrete-Time LTI Systems 507 Memory, 508 Invertibility, 508 Causality, 508 Stability, 509 Unit Step Response, 511 10.4 Difference-Equation Models 512 Difference-Equation Models, 512 Classical Method, 514 Solution by Iteration, 519 10.5Terms in the Natural Response 520 Stability, 521 10.6 Block Diagrams 523 Two Standard Forms, 525 10.7 System Response for Complex-Exponential Inputs 529 Linearity, 530 Complex Inputs for LTI Systems, 530 Stability, 535 Sampled Signals, 535 Impulse Response, 535 Summary 537 Problems 538 11 The z-Transform 547 11.1 Definitions of z-Transforms 547 11.2 Examples 550 Two z-Transforms, 550 Digital-Filter Example, 553 11.3 z-Transforms of Functions 555 Sinusoids, 557 11.4 z-Transform Properties 560 Real Shifting, 560 Initial and Final Values, 56311.5 Additional Properties 565 Time Scaling, 565 Convolution in Time, 567 11.6 LTI System Applications 568 Transfer Functions, 569 Inverse z-Transform, 571Complex Poles, 574 Causality, 575 Stability, 576 Invertibility, 579 11.7 Bilateral z-Transform 580 Bilateral Transforms, 585 Regions of Convergence, 586 Inverse Bilateral Transforms, 588 Summary 590 Problems 591 12 Fourier Transformsof Discrete-Time Signals 599 12.1 Discrete-Time Fourier Transform 600 z-Transform, 602 12.2 Properties of the Discrete-Time Fourier Transform 605 Periodicity, 605 Linearity, 606 Time Shift, 606 Frequency Shift, 607 Symmetry, 608 TimeReversal, 608 Convolution in Time, 609 Convolution in Frequency, 609 Multiplication by n, 610 Parseval's Theorem, 610 12.3 Discrete-Time Fourier Transform of Periodic Sequences 611 12.4 Discrete Fourier Transform 617 Shorthand Notation for the DFT, 620 Frequency Resolution of the DFT, 621 Validity of the DFT, 622 Summary, 626 12.5 Fast Fourier Transform 627 Decomposition-in-Time Fast Fourier Transform Algorithm, 627 Decomposition-in-Frequency Fast Fourier Transform, 632 Summary, 635 12.6 Applications of the Discrete Fourier Transform 635 Calculation of Fourier Transforms, 635 Convolution, 646 Filtering, 653 Correlation, 660 Energy Spectral Density Estimation, 666 Summary, 667 12.7 The Discrete Cosine Transform, 667 Summary 669 Problems 671 13 State Variables for Discrete-Time Systems 677 13.1 State-Variable Modeling 678 13.2 Simulation Diagrams 682 13.3 Solution of State Equations 688 Recursive Solution, 688 z-Transform Solution, 690 13.4 Properties of the State Transition Matrix 695 13.5 Transfer Functions 697 Stability, 699 13.6 Similarity Transformations 700 Properties, 704 Summary 705 Problems 707 Appendices 714 A. Integrals and Trigonometric Identities 714 Integrals, 714 Trigonometric Identities, 715 B. Leibnitz's and L'Hopital's Rules 716 Leibnitz's Rule, 716 L'Hopital's Rule, 717 C. Summation Formulas for Geometric Series 718 D. Complex Numbers and Euler's Relation 719 Complex-Number Arithmetic, 720 Euler's Relation, 723 Conversion Between Forms, 724E. Solution of Differential Equations 726 Complementary Function, 726 Particular Solution, 727 General Solution, 728 Repeated Roots, 728 F. Partial-Fraction Expansions 730 G. Review of Matrices 733 Algebra of Matrices, 737 Other Relationships, 738 H. Answers to Selected Problems 740 I. Signals and Systems References 750 Index 759

• ISBN: 978-0-13-206742-3
• Editorial: Pearson/Prentice Hall
• Encuadernacion: Rústica
• Páginas: 784
• Fecha Publicación: 01/01/2008
• Nº Volúmenes: 1
• Idioma: Inglés