Fundamentals of Signals and Systems Using The Web and MATLAB

Fundamentals of Signals and Systems Using The Web and MATLAB

1. FUNDAMENTAL CONCEPTS 1

1.1 Signals and Systems 1

1.2 Continuous-Time Signals 6

1.3 Discrete-Time Signals 17

1.4 Examples of Systems 25

1.5 Basic System Properties 36

Problems 47

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2. SYSTEMS DEFINED BY DIFFERENTIAL OR DIFFERENCE EQUATIONS 57

2.1 Linear Input/Output Differential Equations with Constant Coefficients 57

2.2 System Modeling 61

2.3 Linear Input/Output Difference Equations with Constant Coefficients 66

2.4 Discretization in Time of Differential Equations 72

2.5 Systems Defined by Time-Varying or Nonlinear Equations 80

Problems 88

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3. CONVOLUTION REPRESENTATION 101

3.1 Convolution Representation of Linear Time-Invariant Discrete-Time Systems 101

3.2 Convolution of Discrete-Time Signals 104

3.3 Convolution Representation of Linear Time-Invariant Continuous-Time Systems 114

3.4 Convolution of Continuous-Time Signals 118

3.5 Numerical Convolution 128

3.6 Linear Time-Varying Systems 132
Problems 134

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4 THE FOURIER SERIES AND FOURIER TRANSFORM 145

4.1 Representation of Signals in Terms of Frequency Components 153

4.2 Fourier Series Representation of Periodic Signals 161

4.3 Fourier Transform 175

4.4 Properties of the Fourier Transform 190

4.5 Generalized Fourier Transform 190

Problems 193

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5 FREQUENCY-DOMAIN ANALYSIS OF SYSTEMS 202

5.1 Response to a Sinusoidal Input 203

5.2 Response to Periodic Inputs 210

5.3 Response to Aperiodic Inputs 216

5.4 Analysis of Ideal Filters 221

5.5 Analysis of Ideal Filters 221

5.6 Sampling 231

Problems 238

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6 APPLICATION TO COMMUNICATIONS 251

6.1 Analog Modulation 252

6.2 Demodulation of Analog Signals 260

6.3 Simultaneous Transmission of Signals 264

6.4 Digital Modulation 268

6.5 Baseband PAM 272

6.6 Passband PAM 276

6.7 Digital Communication Simulations 282

Problems 289

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ex6_1	ex6_11	PAM1
ex6_2	ex6_12	PAM2
ex6_3	ex6_13	FSK
ex6_5	fig6_40

7 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 297

7.1 Discrete-Time Fourier Transform 298

7.2 Discrete Fourier Transform 310

7.3 Properties of the DFT 322

7.4 System Analysis via the DTFT and DFT 331

7.5 FFT Algorithm 339

7.6 Applications of the FIT Algorithm 341

Problems 349

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ex7_8.m	ex7_11.m	ex7_16.m
ex7_9.m	ex7_12.m	fig7_2.m
ex7_10.m	ex7_15.m	fig7_5.m

8 THE LAPLACE TRANSFORM AND THE TRANSFER FUNCTION REPRESENTATION 358

8.1 Laplace Transform of a Signal 359

8.2 Properties of the Laplace Transform 363

8.3 Computation of the Inverse Laplace Transform 374

8.4 Transform of the Input/Output Differential Equation 394

8.5 Transfer Function Representation 401

8.6 Transfer Function of Block Diagrams 415

Problems 423

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9 SYSTEM ANALYSIS USING THE TRANSFER FUNCTION REPRESENTATION 435

9.1 Stability and the Impulse Response 436

9.2 Routh-Hurwitz Stability Test 439

9.3 Analysis of the Step Response 443

9.4 Response to Sinusoids and Arbitrary Inputs 459

9.5 Frequency Response Function 465

9.6 Causal Filters 484

Problems 498

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ex9_7.m	ex9_17.m	fig9_20.m
ex9_8.m	ex9_20.m	fig9_22.m
ex9_9.m	ex9_22.m	fig9_25.m
ex9_10.m	ex9_23.m	fig9_26.m
ex9_11.m	ex9_25.m	fig9_29.m
ex9_12.m	ex9_26.m	fig9_30.m
ex9_13.m	ex9_27.m	fig9_36.m
ex9_14.m	ex9_28.m	fig9_38.m
ex9_16.m	fig9_18.m	fig9_39.m

 

10 APPLICATION TO CONTROL 509

10.1 Introduction to Control 509

10.2 Tracking Control 516

10.3 Root Locus 527

10.4 Application to Control System Design 535

Problems 543

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ex10_2.m	ex10_8.m
ex10_3.m	ex10_9.m
ex10_4.m	ex10_10.m
ex10_5.m	ex10_11.m
ex10_7.m	ex10_12.m

11 THE Z-TRANSFORM AND DISCRETE-TIME SYSTEMS 555

11.1 z-Transform of a Discrete-Time Signal 556

11.2 Properties of the z-Transform 560

11.3 Computation of the Inverse z-Transform 571

11.4 Transfer Function Representation 581

11.5 Stability of Discrete-Time Systems 593

11.6 Frequency Response of Discrete-Time Systems 597

Problems 601

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12 DESIGN OF DIGITAL FILTERS AND CONTROLLERS 612

12.1 Discretization 613

12.2 Design of IIR Filters 618

12.3 Design of IIR Filters Using MATLAB 623

12.4 Design of FIR Filters 630

12.5 Design of Digital Controllers 643

Problems 649

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ex12_1.m	ex12_7.m	fig12_4.m
ex12_2.m	ex12_8.m	fig12_13.m
ex12_3.m	ex12_9.m	fig12_14.m
ex12_4.m	ex12_10.m	fig12_20.m
ex12_5.m	ex12_11.m	fig12_21.m
ex12_6.m	ex12_12.m

13 STATE REPRESENTATION 655

13.1 State Model 656

13.2 Construction of State Models 659

13.3 Solution of State Equations 667

13.4 Discrete-Time Systems 676

13.5 Equivalent State Representations 683

13.6 Discretization of State Model 689

Problems 692

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