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أخواني في الله أحضرت لكم كتاب Signals and Systems Using MATLAB Third Edition Luis F. Chaparro Department of Electrical and Computer Engineering University of Pittsburgh Pittsburgh, PA, USA Aydin Akan Department of Biomedical Engineering Izmir Katip Celebi University Izmir, Turkey
![كتاب Signals and Systems Using MATLAB M_s_a_17](https://i.servimg.com/u/f61/15/36/74/14/m_s_a_17.jpg) و المحتوى كما يلي :
CHAPTER FROM THE GROUND UP! CONTENTS 0.1 Introduction 4 0.2 Examples of Signal Processing Applications . 4 0.2.1 Compact-Disc (CD) Player . 5 0.2.2 Software-Defined Radio and Cognitive Radio . 6 0.2.3 Computer-Control Systems . 7 0.3 Implementation of Digital Signal Processing Algorithms . 8 0.3.1 Microprocessors and Micro-Controllers 9 0.3.2 Digital Signal Processors . 9 0.3.3 Field Programmable Gate Arrays 9 0.4 Continuous or Discrete? 10 0.4.1 Continuous and Discrete Representations . 11 0.4.2 Derivatives and Finite Differences 12 0.4.3 Integrals and Summations . 14 0.4.4 Differential and Difference Equations 16 How to Solve Ordinary Differential Equations . 18 0.5 Complex or Real? . 20 0.5.1 Complex Numbers and Vectors 21 Euler’s Identity 24 0.5.2 Functions of a Complex Variable 27 0.5.3 Phasors and Sinusoidal Steady State 28 0.5.4 The Phasor Connection . 30 0.6 Soft Introduction to MATLAB 32 0.6.1 Numerical Computations . 33 MATLAB as a Calculator 33 MATLAB as a Signal Generator 37 Saving and Loading Data . 40 0.6.2 Symbolic Computations 41 Derivatives and Differences 43 The Sinc Function and Integration 44 Chebyshev Polynomials and Lissajous Figures . 46 Ramp, Unit-Step and Impulse Responses 49 0.7 Problems . 50 0.7.1 Basic Problems 50 0.7.2 Problems Using MATLAB CHAPTER CONTINUOUS-TIME SIGNALS CONTENTS 1.1 Introduction 59 1.2 Classification of Time-Dependent Signals 60 1.3 Continuous-Time Signals 61 1.3.1 Addition, Constant Multiplication, Time Shifting and Reflection 65 1.3.2 Even and Odd Signals 68 1.3.3 Periodic and Aperiodic Signals 70 1.3.4 Finite-Energy and Finite-Power Signals 72 Superposition of Power 76 1.4 Representation of Continuous-Time Signals Using Basic Signals 77 1.4.1 Complex Exponentials 78 Sinusoids . 79 1.4.2 Unit Step, Unit Impulse and Ramp Signals . 80 The Ramp Signal . 82 Signal Generation With MATLAB 83 1.4.3 Generic Representation of Signals 91 1.5 Time Scaling, Modulation, Windowing and Integration . 93 1.6 Special Signals—the Sampling and the Sinc Signals 102 1.7 What Have We Accomplished? Where Do We Go From Here? . 104 1.8 Problems . 105 1.8.1 Basic Problems 105 1.8.2 Problems Using MATLAB . CHAPTER CONTINUOUS-TIME SYSTEMS CONTENTS 2.1 Introduction 115 2.2 System Concept and Classification 116 2.3 Linear Time-Invariant (LTI) Continuous-Time Systems 117 2.3.1 Linearity 118 The Op-Amp 122 2.3.2 Time-Invariance 123 AM Communication System 124 FM Communication System 125 Vocal System 125 2.3.3 Representation of Systems by Ordinary Differential Equations . 128 2.4 The Convolution Integral . 135 2.4.1 Impulse Response and Convolution Integral 137 2.4.2 Interconnection of Systems—Block Diagrams 144 2.5 Causality 148 2.5.1 Graphical Computation of Convolution Integral . 150 2.6 Bounded Input–Bounded Output Stability . 154 2.7 What Have We Accomplished? Where Do We Go From Here? . 157 2.8 Problems . 158 2.8.1 Basic Problems 158 2.8.2 Problems Using MATLAB . CHAPTER THE LAPLACE TRANSFORM CONTENTS 3.1 Introduction 167 3.2 The Two-Sided Laplace Transform . 169 3.2.1 Eigenfunctions of LTI Systems 169 3.2.2 Region of Convergence . 173 Poles and Zeros and the Region of Convergence . 174 Poles and Region of Convergence . 175 3.3 The One-Sided Laplace Transform . 178 3.4 Properties of the One-Sided Laplace Transform . 186 3.4.1 Linearity 187 3.4.2 Differentiation . 190 3.4.3 Integration . 193 3.4.4 Time-Shifting 194 3.4.5 Duality 196 3.4.6 Convolution Integral 199 3.5 Inverse Laplace Transform 200 3.5.1 Inverse of One-Sided Laplace Transforms . 201 Simple Real Poles . 203 Simple Complex Conjugate Poles 204 Double Real Poles . 208 3.5.2 Inverse of Functions Containing e−ρs Terms . 212 3.6 The Transfer Function of LTI Systems . 213 3.7 Analysis of LTI Systems Represented by Differential Equations . 220 Zero-State and Zero-Input Responses 222 Transient and Steady-State Responses . 223 3.8 Inverse of Two-Sided Laplace Transforms 227 3.9 What Have We Accomplished? Where Do We Go From Here? . 230 3.10 Problems . 230 3.10.1 Basic Problems 230 3.10.2 Problem Using MATLAB CHAPTER FREQUENCY ANALYSIS: THE FOURIER SERIES CONTENTS 4.1 Introduction 241 4.2 Eigenfunctions Revisited . 242 4.3 Complex Exponential Fourier Series . 249 4.3.1 Line Spectrum—Power Distribution Over Frequency 252 Parseval’s Power Relation 252 Symmetry of Line Spectra 253 4.3.2 Trigonometric Fourier Series . 254 4.3.3 Fourier Series and Laplace Transform 258 4.3.4 Reflection and Even and Odd Periodic Signals . 260 4.3.5 Convergence of the Fourier Series 274 4.3.6 Time and Frequency Shifting 278 4.4 Response of LTI Systems to Periodic Signals 281 4.4.1 Filtering of Periodic Signals . 284 4.5 Operations Using Fourier Series 287 4.5.1 Sum of Periodic Signals 287 4.5.2 Multiplication of Periodic Signals 288 4.5.3 Derivatives and Integrals of Periodic Signals . 290 4.5.4 Amplitude and Time Scaling of Periodic Signals . 292 4.6 What Have We Accomplished? Where Do We Go From Here? . 296 4.7 Problems . 297 4.7.1 Basic Problems 297 4.7.2 Problems Using MATLAB . CHAPTER FREQUENCY ANALYSIS: THE FOURIER TRANSFORM CONTENTS 5.1 Introduction 305 5.2 From the Fourier Series to the Fourier Transform . 306 5.3 Existence of the Fourier Transform 308 5.4 Fourier Transforms From the Laplace Transform . 309 5.5 Linearity, Inverse Proportionality and Duality 310 5.5.1 Linearity 310 5.5.2 Inverse Proportionality of Time and Frequency . 311 5.5.3 Duality 317 5.6 Spectral Representation . 319 5.6.1 Signal Modulation 319 Why Amplitude Modulation? 322 5.6.2 Fourier Transform of Periodic Signals 323 5.6.3 Parseval’s Energy Relation . 325 5.6.4 Symmetry of Spectral Representations 327 5.7 Convolution and Filtering 332 5.7.1 Basics of Filtering 334 5.7.2 Ideal Filters 336 5.7.3 Frequency Response From Poles and Zeros 341 5.7.4 The Spectrum Analyzer 346 5.8 Additional Properties . 348 5.8.1 Time Shifting 348 5.8.2 Differentiation and Integration 349 5.9 What Have We Accomplished? What Is Next? . 352 5.10 Problems . 353 5.10.1 Basic Problems 353 5.10.2 Problems Using MATLAB CHAPTER APPLICATION OF LAPLACE ANALYSIS TO CONTROL CONTENTS 6.1 Introduction 363 6.2 System Connections and Block Diagrams . 364 6.3 Application to Classical Control 368 6.3.1 Stability and Stabilization . 373 6.3.2 Transient Analysis of First- and Second-Order Control Systems 375 6.4 State-Variable Representation of LTI Systems . 382 6.4.1 Canonical Realizations . 389 6.4.2 Complete Solution From State and Output Equations . 396 Exponential Matrix Solution 396 Cramer’s Rule Solution 397 6.4.3 External and Internal Representation of Systems 399 6.5 What Have We Accomplished? What Is Next? . 402 6.6 Problems . 403 6.6.1 Basic Problems 403 6.6.2 Problems Using MATLAB . CHAPTER FOURIER ANALYSIS IN COMMUNICATIONS AND FILTERING CONTENTS 7.1 Introduction 409 7.2 Application to Communications . 410 7.2.1 AM Suppressed Carrier (AM-SC) 411 7.2.2 Commercial AM 413 7.2.3 AM Single Sideband 415 7.2.4 Quadrature AM and Frequency Division Multiplexing 416 Quadrature Amplitude Modulation (QAM) 416 Frequency Division Multiplexing (FDM) . 417 7.2.5 Angle Modulation 418 7.3 Analog Filtering . 421 7.3.1 Filtering Basics 423 Magnitude Squared Function 423 Filter Specifications 424 7.3.2 Butterworth Low-Pass Filter Design 425 Factorization . 426 Filter Design . 427 7.3.3 Chebyshev Low-Pass Filter Design 429 Filter Design . 430 Factorization . 431 7.3.4 Frequency Transformations 434 7.3.5 Filter Design With MATLAB 436 Low-Pass Filter Design 436 General Filter Design 439 7.4 What Have We Accomplished? What Is Next? . 440 7.5 Problems . 441 7.5.1 Basic Problems 441 7.5.2 Problems Using MATLAB CHAPTER SAMPLING THEORY CONTENTS 8.1 Introduction 449 8.2 Uniform Sampling . 450 8.2.1 Pulse Amplitude Modulation 450 8.2.2 Ideal Impulse Sampling 451 8.2.3 Reconstruction of the Original Continuous-Time Signal . 459 8.2.4 Signal Reconstruction From Sinc Interpolation . 462 8.2.5 The Nyquist–Shannon Sampling Theorem . 463 8.2.6 Sampling Simulations With MATLAB . 464 8.2.7 Sampling Modulated Signals 468 8.3 Practical Aspects of Sampling 469 8.3.1 Sample-and-Hold Sampling . 470 8.3.2 Quantization and Coding . 472 8.3.3 Sampling, Quantizing and Coding With MATLAB . 474 8.4 Application to Digital Communications 477 8.4.1 Pulse Code Modulation . 478 Baseband and Band-Pass Communication Systems . 480 8.4.2 Time-Division Multiplexing . 481 8.5 What Have We Accomplished? Where Do We Go From Here? . 482 8.6 Problems . 482 8.6.1 Basic Problems 482 8.6.2 Problems Using MATLAB . CHAPTER DISCRETE-TIME SIGNALS AND SYSTEMS CONTENTS 9.1 Introduction 487 9.2 Discrete-Time Signals 488 9.2.1 Periodic and Aperiodic Discrete-Time Signals 490 9.2.2 Finite-Energy and Finite-Power Discrete-Time Signals 494 9.2.3 Even and Odd Discrete-Time Signals . 497 9.2.4 Basic Discrete-Time Signals . 500 Discrete-Time Complex Exponential 500 Discrete-Time Sinusoids 503 Discrete-Time Unit-Step and Unit-Sample Signals 506 Generic Representation of Discrete-Time Signals 507 9.3 Discrete-Time Systems . 511 9.3.1 Recursive and Non-recursive Discrete-Time Systems 514 9.3.2 Dynamic Discrete-Time Systems Represented by Difference Equations 518 9.3.3 The Convolution Sum . 519 9.3.4 Linear and Non-linear Filtering With MATLAB 525 Linear Filtering 526 Non-linear Filtering 526 9.3.5 Causality and Stability of Discrete-Time Systems 529 Causality . 529 Bounded Input–Bounded Output (BIBO) Stability . 531 9.4 Two-Dimensional Discrete Signals and Systems . 532 9.4.1 Two-Dimensional Discrete Signals 532 9.4.2 Two-Dimensional Discrete Systems . 537 9.5 What Have We Accomplished? Where Do We Go From Here? . 543 9.6 Problems . 543 9.6.1 Basic Problems 543 9.6.2 Problems Using MATLAB . CHAPTER THE Z-TRANSFORM CONTENTS 10.1 Introduction 559 10.2 Laplace Transform of Sampled Signals . 560 10.3 Two-Sided Z-transform . 563 10.3.1 Region of Convergence . 564 ROC of Finite-Support Signals 565 ROC of Infinite-Support Signals . 567 10.4 One-Sided Z-transform . 569 10.4.1 Signal Behavior and Poles . 569 10.4.2 Computing Z-transforms With Symbolic MATLAB 573 10.4.3 Convolution Sum and Transfer Function . 574 10.4.4 Interconnection of Discrete-Time Systems 583 10.4.5 Initial- and Final-Value Properties 583 10.5 One-Sided Z-transform Inverse . 586 10.5.1 Long-Division Method 586 10.5.2 Partial Fraction Expansion . 587 10.5.3 Inverse Z-transform With MATLAB . 591 Partial Fraction Expansion . 591 A. Simple Poles 592 B. Multiple Poles 593 10.5.4 Solution of Difference Equations . 595 Approximate Solution of Ordinary Differential Equations 602 10.5.5 Inverse of Two-Sided Z-transforms . 604 10.6 State Variable Representation 606 Solution of the State and Output Equations 610 Canonical Realizations . 614 10.7 Two-Dimensional Z-transform . 618 10.8 What Have We Accomplished? Where Do We Go From Here? . 627 10.9 Problems . 627 10.9.1 Basic Problems 627 10.9.2 Problems Using MATLAB CHAPTER DISCRETE FOURIER ANALYSIS CONTENTS 11.1 Introduction 638 11.2 The Discrete-Time Fourier Transform (DTFT) . 639 11.2.1 Sampling, Z-transform, Eigenfunctions and the DTFT 639 11.2.2 Duality in Time and in Frequency 641 11.2.3 Computation of the DTFT Using MATLAB . 644 11.2.4 Time and Frequency Supports 647 11.2.5 Decimation and Interpolation . 648 11.2.6 Energy/Power of Aperiodic Discrete-Time Signals 654 11.2.7 Time and Frequency Shifts 655 11.2.8 Symmetry 656 Computation of the Phase Spectrum Using MATLAB 659 11.2.9 Convolution Sum 662 11.3 Fourier Series of Discrete-Time Periodic Signals . 663 Circular Representation of Discrete-Time Periodic Signals 665 11.3.1 Complex Exponential Discrete Fourier Series . 665 11.3.2 Connection With the Z-transform . 668 11.3.3 DTFT of Periodic Signals 669 Computation of the Fourier Series Using MATLAB . 670 11.3.4 Response of LTI Systems to Periodic Signals . 671 11.3.5 Circular Shifting and Periodic Convolution . 673 11.4 The Discrete Fourier Transform (DFT) . 680 11.4.1 DFT of Periodic Discrete-Time Signals . 680 11.4.2 DFT of Aperiodic Discrete-Time Signals . 681 11.4.3 Computation of the DFT via the FFT . 683 11.4.4 Linear and Circular Convolution 688 11.4.5 The Fast Fourier Transform Algorithm . 693 Radix-2 FFT Decimation-in-Time Algorithm 695 11.4.6 Computation of the Inverse DFT 698 11.5 Two-Dimensional Discrete Transforms 701 11.6 What Have We Accomplished? Where Do We Go From Here? . 708 11.7 Problems . 708 11.7.1 Basic Problems 708 11.7.2 Problems Using MATLAB . CHAPTER INTRODUCTION TO THE DESIGN OF DISCRETE FILTERS CONTENTS 12.1 Introduction 722 12.2 Frequency Selective Discrete Filters 723 12.2.1 Phase Distortion . 724 Group Delay 725 12.2.2 IIR and FIR Discrete Filters . 726 12.3 Filter Specifications 731 12.3.1 Frequency Specifications 731 Loss Function 732 Magnitude Normalization 733 Frequency Scales . 734 12.3.2 Time Domain Specifications . 735 12.4 IIR Filter Design . 736 12.4.1 Transformation Design of IIR Discrete Filters . 736 The Bilinear Transformation . 736 Frequency Warping . 738 12.4.2 Design of Butterworth Low-Pass Discrete Filters . 740 12.4.3 Design of Chebyshev Low-Pass Discrete Filters 748 12.4.4 Rational Frequency Transformations . 753 Low-Pass to Low-Pass Transformation 753 Low-Pass to High-Pass Transformation . 755 Low-Pass to Band-Pass and Low-Pass to Band-Stop Transformations . 756 12.4.5 General IIR Filter Design With MATLAB . 757 12.5 FIR Filter Design 760 12.5.1 Window Design Method 761 12.5.2 Window Functions 763 12.5.3 Linear Phase and Symmetry of the Impulse Response 765 12.6 Realization of Discrete Filters 771 12.6.1 Realization of IIR Filters . 772 Direct Form Realization 772 Cascade Realization 775 Parallel Realization 777 12.6.2 Realization of FIR Filters 779 12.7 Two-Dimensional Filtering of Images 780 12.7.1 Spatial Filtering . 781 12.7.2 Frequency Domain Filtering . 785 12.8 What Have We Accomplished? Where Do We Go From Here? . 793 12.9 Problems . Index A Acoustic signal, 5, 61, 93, 124, 553, 751 Adder circuit, 148 Adders, 65, 123, 147, 367, 384, 403, 607, 771 Aliasing, 466, 650 All-pass filter, 237, 344, 374, 650, 672, 714, 724, 753, 791 ideal, 337 Alternating current (AC), 124 Amplitude analog, 60 maximum, 293 Amplitude modulation (AM), 94 demodulation, 411 envelope detector, 413 suppressed carrier, 411 tunable bandpass filter, 411 Analog communication systems, 410 AM, 410 angle modulation, 418 channel noise, 412 FM, 418 frequency division multiplexing (FDM), 416 quadrature amplitude modulation (QAM), 416 single sideband AM, 415 Analog control systems, 368 actuator, 370 cruise control, 371 feedback, 368 open- and closed-loop, 368 PI controller, 371 positive- and negative-feedback, 367 proportional (P) controller, 375 stability and stabilization, 373 transducer, 370 Analog filtering, 421 basics, 423 Butterworth low-pass filter, 427 Chebyshev low-pass filter, 429 Chebyshev polynomials, 430 eigenfunction property, 423 factorization, 424 frequency transformations, 434 loss function, 424 low-pass specifications, 424 magnitude and frequency normalization, 426 magnitude squared function, 423 Analog LTI systems, 117 BIBO stability, 148, 154, 531, 641, 727 causality, 148, 149 convolution integral, 137 eigenfunction property, 242 frequency response, 242, 333 impulse response, 137 impulse response, transfer function and frequency response, 333 passivity, 155 transient analysis, 375 zero-input response, 128 zero-state response, 128 Analog systems dc source, 335 windowing, 335 Analog-to-digital converter A/D converter, 470 Antenna, 6, 124, 322 Antialiasing filter, 460 Application-specific integrated circuit (ASIC), 4 Armstrong, E., 418 Attenuation, 113, 233, 338, 444, 627, 729 B Basic analog signal operations adding, 65 advancing and delaying, 65 constant multiplying, 65 modulation, 93 reflection, 65 time scaling, 93 Basic analog signals complex exponentials, 78 ramp, 82 sinusoids, 79 triangular pulse, 88 809810 Index unit-impulse, 80 unit-step, 81 Basic discrete-time signals complex exponentials, 500 sinusoids, 503 unit-step and unit-sample signals, 506 Bilinear transformation, 738 warping, 738 Biological systems, 4, 489 C Capability of storing energy, 116, 127, 383 Capacitance, 116, 159 Capacitors, 8, 17, 30, 115, 125, 155, 423 Carrier, 124, 410 Cascade connections, 144, 365, 410, 521 Chemical plant, 363 Chirp signal, 43, 114, 715 Circuit open, 17, 163, 340 short, 163, 340 Circuit theory, 72, 332, 412 Circular shifting, 673 Classical control, 158, 368, 402 Clock frequencies, 9 Closed-loop transfer function, 364 Comb filters, 730, 799 Complex conjugate poles, 188, 205, 237, 776 Complex variables, 20 function, 27 Continuous-time LTI systems complete response, 223 eigenfunction property, 169 represented by ordinary differential equations, 220 steady-state response, 223 transient response, 223 unit-step response, 225 zero-input response, 222 zero-state, zero-input responses, 222 zero-state response, 222 Continuous-time signals absolutely integrable, 73 advanced, 66 aperiodic, 60, 70 basic signals, 77 causal sinusoid, 74 complex exponentials, 77 definition, 62 delayed, 66 even, 60, 66, 68 even and odd decomposition, 69 finite energy, 60, 72 finite power, 60, 72, 73 finite support, 60 full-wave rectified, 88 odd, 60, 66, 68 periodic, 60, 70 real and imaginary parts, 78 shifting and reflecting, 67 sinusoids, 64 speech, 62 square integrable, 73 train of rectangular pulses, 89 windowing, 65 Conversion, 5, 23, 61, 360, 474 Convolution integral commutative property, 145 distributive property, 145 Fourier, 332 graphical computation, 150 Laplace, 213 Convolution sum, 519, 574 commutative property, 521 deconvolution, 521 graphical, 576 length, 575 noncausal signals, 580 Cooley, J., 694 Cramer’s rule, 396, 611 Cut-off frequencies, 335 D D/A converter, 62 Damped sinusoid, 78, 95, 501 Damping factor, 20, 168, 189, 560 Dc gain, 299, 425, 629, 746, 794 Dc loss, 425, 433, 733, 747, 799 Dc source, 20, 50, 267, 294, 335, 359, 546 De Moivre, A., 563 Differentiation, 12, 81, 190, 349 Digital communications, 477 PCM, 477 time-division multiplexing, 481 Digital signal processing FFT, 693 inverse FFT, 698Index 811 Digital-to-analog converter D/A converter, 62, 470 Dirac, P., 178 Discrete Cosine Transform (DCT) 1D-DCT, 704 2D-DCT, 706 transform coding, 704 Discrete filtering analog signals, 723 averaging filter, 526 bilinear transformation, 736 Butterworth LPF, 740 Chebyshev LPF, 748 eigenfunction property of LTI systems, 723 FIR realizations, 779 FIR window design, 761 frequency scales, 734 frequency selective filters, 723 frequency specifications, 731 group delay, 725 IIR and FIR, 726 IIR realizations, 772 linear phase, 724 loss function, 732 median filter, 527 rational frequency transformations, 753 realization, 771 time specifications, 735 windows for FIR design, 763 Discrete filters FIR, 582 FIR filters and convolution sum, 575 IIR, 582 Discrete Fourier series, 663 circular representation, 665 circular shifting, 673 complex exponential, 665 periodic convolution, 673 Z-transform, 668 Discrete Fourier Transform (DFT), 680 Fast Fourier Transform (FFT), 683 linear and circular convolution, 688 Discrete LTI systems autoregressive (AR), 515 autoregressive moving average (ARMA), 517 BIBO stability, 529, 581 causality, 529 convolution sum, 519 difference equation representation, 514 moving average (MA), 514 recursive (IIR) and non-recursive (FIR), 514 response to periodic signals, 671 time-invariance, 512 Discrete-Time Fourier Transform (DTFT), 639 convergence, 639 convolution sum, 662 decimation, 648 eigenfunctions, 640 interpolation, 648 Parseval’s theorem, 654 periodic signals, 669 sampled signal, 640 symmetry, 656 time and frequency shifts, 655 time–frequency duality, 641 time–frequency supports, 647 Z-transform, 640 Discrete-time signals absolutely summable, 494 definition, 488 discrete frequency, 500 energy and power spectrum, 654 Fibonacci sequence, 489 finite energy, 494 finite power, 494 generic representation, 507 inherently discrete-time, 489 periodic, fundamental period, 490 sample index, 489 sinusoid, 489 square summable, 494 square summable, finite energy, 494 Discrete-time sinusoids, 503, 544, 656 periodic, 490 Discretization, 11, 62, 560, 644 Disturbance, 7, 368, 691 Doppler frequency shift, 113, 444 Double poles, 189, 572 Double real poles, 208, 379 Down-sampling, 500, 552, 649, 715, 800 E Electrical circuit, 8 Electronic noise, 7, 17 Elliptic design, 439 Elliptic filters, 445, 798812 Index Energy conservation property, 326 consumption, 7 continuous-time signals, 73 discrete-time signals, 494 spectrum, 326, 654 Euler, L., 23 Euler’s identity, 23, 78 F Fast Fourier Transform (FFT), 693 inverse, 698 Fessenden, R., 124 Filtering, 245 analog basics, 334 antialiasing, 455 RC high-pass filter, 343 RC low-pass filter, 342 Filters band-stop, 340, 435, 753, 781 bandpass, 340, 412, 440 comb, 730 denormalized, 426, 427 frequency discriminating, 334 gaussian, 720, 782 ideal, 299, 336 linear, 525, 785 magnitude-normalized, 425 median, 527 non-linear, 525 Finite calculus, 10 finite-difference, 12 summations, 14 Fourier, J.B., 249 Fourier series absolute uniform convergence, 274 analog Parseval’s power relation, 252 coefficients, 250 coefficients from Laplace, 258 complex exponential, 249 convergence, 274 dc component, 255 even and odd signals, 260 Fourier basis, 251 fundamental frequency, 250 fundamental period, 250 Gibb’s phenomenon, 274 harmonics, 255 line spectrum, 253 mean-square approximation, 275 normality, 251 orthogonality, 251 periodic signals, 243 product of periodic signals, 288 spectrum analyzer, 252 sum of periodic signals, 287 time and frequency shifting, 278 time reversal, 260 trigonometric, 254 Fourier transform amplitude modulation, 320 analog spectrum and line spectrum, 323 convolution integral, 332 differentiation and integration, 349 direct and inverse, 307 duality, 317 frequency shifting, 319 Laplace ROC, 309 linearity, 310 periodic analog signals, 323 shifting in time, 348 symmetry, 327 Frequencies carrier, 412 instantaneous, 114, 419 normalized, 423 passband, 440 stopband, 445, 731 Frequency modulation (FM) definition, 94 Frequency response poles and zeros, 341 G Gauss, C., 15, 701 Gaussian filter, 720, 782 Gaussian noise, 526, 659 Gibbs phenomenon filtering, 339 Global positioning system (GPS), 4 H Harmonic frequencies, 253, 285, 323, 671 Heaviside, O., 169 Hertz, H., 28 Human visual system, 781Index 813 I Ideal filters band-pass, 336 band-pass and high-pass, 336 high-pass, 336 linear phase, 336 low-pass, 336 zero-phase, 338 Image processing 2D filtering, 781 bank of filters, 790 binarization, 704 data compression, 704, 790 edge detection, 782 non-linear filtering, 785 Image processing, edge detection, 556 Images digital, 534 discretized, 534 Inductors, 8, 30, 115, 125, 155, 423 Instability, 375 Integration, 14, 93, 100, 120, 193, 258, 272, 349, 361, 638 Inverse Laplace partial fraction expansion, 201 two-sided, 227 with exponentials, 212 Inverse proportionality, 310 Inverse Z-transform inspection, 586 long-division method, 586 partial fraction expansion, 587 positive powers of z, 590 proper rational functions, 587 rational functions, 587 J Jury, E.I., 563 K Kalman filtering, 563 L Laplace, P.S., 169 Laplace transform convolution integral, 199 derivative, 190 integration, 193 inverse, 171, 200 linearity, 187 poles and zeros, 174 proper rational, 201 region of convergence (ROC), 174 sampled signals, 560 two-sided, 171 L’Hôpital’s rule, 264 M Marconi, G., 124 MATLAB analog Butterworth and Chebyshev filter design, 434 analog Butterworth filtering, 433 control toolbox, 379 decimation and interpolation, 650 DFT and FFT, 644 discrete filter design, 749 DTFT computation, 644 FFT computation, 700 filter design, 436 Fourier series computation, 670 general discrete filter design, 757 numerical computations, 33 phase computation, 659 phase unwrapping, 659 spectrogram, 421 symbolic computations, 43 window FIR filter design, 771 Maximum frequency, 454 Message, 124, 161, 172, 320, 410, 468, 477 analog, 450, 477 digital, 450, 477 N Noise, 7, 17, 165, 334, 526, 659, 781 Noisy signal, 13, 481, 527, 630 Non-linear filtering median filter, 527 Nyquist sampling rate, 464 sampling theorem, 463 Nyquist, H., 464 P Parallel connections, 144, 364, 410 Phase modulation (PM) definition, 94 Phasor connection, 30814 Index Phasors sinusoidal steady state, 244 Plant, 7, 363, 585 Pole–zero cancellation, 186, 223, 374, 399, 761 Power, 72, 73 average, 73 discrete-time signals, 494 instantaneous, 72 Power spectral density, 183 Pulse amplitude modulation (PAM), 450 code modulation (PCM), 477 Q Quantization error, 473 four-level quantizer, 472 step, 473 R Radio spectrum, 6, 416, 450, 477 Real-time processing, 65 Recursive system, 514, 540 Reference signal, 7, 239, 368, 407, 585 Resistance, 110, 116, 159 Resistors, 8, 17, 72, 107, 115, 120, 147, 155, 246, 340, 403, 423 S Sampler time-varying system, 453 Sampling antialiasing filter, 455, 460 band-limited signal, 454 Discrete-Time Fourier Transform, 453 frequency aliasing, 455 holder for D/A, 471 ideal impulse, 451 Nyquist rate, 464 Nyquist–Shannon theorem, 463 Parseval’s application, 458 practical aspects, 469 quantization, 472 quantization error, 472, 473 quantizer, 472 sample-and-hold system, 470 sampling frequency, 454 sampling function, 451 signal reconstruction, 459 sinc interpolation, 462 time-division multiplexing, 481 uniform sampling, 450 Shannon, C., 464 Signal processing applications cognitive radio, 6 compact-disc (CD) player, 5 computer-control systems, 7 software-defined radio, 6 Signal processing system, 8 analog-to-digital converter, 8 digital signal processors (DSPs), 4, 8 field-programmable gate arrays (FPGAs), 4, 8 microprocessors and micro-controllers, 8 real-time implementation, 8 Signals absolutely summable, 494 analog, 60 band-limited, 454 causal, anticausal, noncausal, 173 causal discrete sinusoid, 494 continuous-time, 60 delayed, 66 deterministic, 60 digital, 60 discrete finite energy, 494 discrete sinusoid, 489 discrete-time, 60 finite energy discrete signal, 494 full-wave rectified, 267 modulation, 124 piecewise smooth, 274 radiated with antenna, 322 random, 60 sampled continuous-time, 489 sinc, 264 smooth, 274 square summable, 494 Sobel filters, 557, 782 Spectrum, 327, 411, 446, 465, 640, 652, 724, 781 Steinmetz, C., 28 Superposition, 76, 118, 135, 203, 244, 333, 417, 453, 512, 664, 682 Support finite, 64, 93, 151, 179, 311, 321, 454, 479, 534, 565, 630, 644, 702 first-quadrant, 624Index 815 infinite, 70, 173, 250, 308, 336, 523, 567, 664 one-point, 311 Switch, 126, 162, 450, 471, 481 System analog, 117 continuous-time, 117 definition, 116 digital, 117 discrete-time, 117 hybrid, 117 System connections, 364 Systems all-pass, 248 amplitude modulation (AM), 124 analog averager, 139 discrete, 482, 560, 638, 693 echo, 155, 161 frequency modulation (FM), 125 ideal communication system, 247 linearity, 118 multi-path channel, 172 negative-feedback, 367, 403 non-linear, 123 positive-feedback, 367 sample-and-hold sampling, 470 single-input single-output, 117 time-invariance, 123 time-varying, 123 unstable, 118, 154, 236, 373 vocal system, 125 zero-order-hold, 470 T Tesla, N., 124 Theorem, initial-value, 202 Transfer function BIBO, 630 constant-numerator, 609, 772 discrete, 737 feedback, 403 feedforward, 376, 403 normalized, 441 one-dimensional, 626 only-zeros, 391 open-loop, 364 rational, 341, 439, 727 representation, 383, 560 two-dimensional, 626 Transient responses, 223, 600 Transmitter, 112, 124, 172, 410, 478 Triangular signal, 88, 142, 271, 292, 300 Tsypkin, Y., 563 Tukey, J., 694 Two-Dimensional Discrete Fourier Transform, 701 2D-FFT, 702 aperiodic signals, 702 Two-dimensional discrete signals, 532 impulse, 533 periodic, 534 rectangular and block periodic, 536 separable, 533 unit-ramp, 533 unit-step, 533 Two-dimensional discrete systems, 532, 537 convolution, 537 FIR, 540 IIR, 540 impulse response, 537 LSI, 537 LSI BIBO, 540 LSI causal, 542 separable, 538 Two-dimensional filtering, 781 1D vs. 2D, 781 circular filters, 788 frequency domain, 786 separable, 787 spatial, 781 Two-dimensional Z-transform, 618 convolution sum, 622 inverse, 621 stability testing, 623 U Unit-step function, 99 V Voice signal, 60, 124, 724 Voltage, 8, 18 ac, 239, 299 dc, 299 Voltage follower, 147, 366, 403 circuit, 147, 403 Voltage source, 17, 127, 148, 154, 192, 216, 246, 339, 376, 441 Voltage–current relation, 120816 Index W Walsh functions, 303 Windowed cosine, 480 Wireless communications, 112, 124, 172, 477 Z Z-transform connection with sampling, 563 damping radius, 562 discrete frequency, 562 inverse, 586 linearity, 569 one-sided, 569 poles and zeros, 587 ROC and uniqueness, 568 s-plane and Z-plane, 562 sampled signals, 561 significance of poles, 573 solution of difference equations, 596, 602 time-shifting, 595 transfer function, 574 two-sided transform, 563 Zadeh, L., 563 Zero-boundary conditions, 537 #ماتلاب,#متلاب,#Matlab,
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