信号处理引论【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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1 Introduction1

1-1 Mathematical Representation of Signals2

1-2 Mathematical Representation of Systems4

1-3 Thinking About Systems5

1-4 The Next Step6

2 Sinusoids7

2-1 Tuning Fork Experiment8

2-2 Review of Sine and Cosine Functions9

2-3 Sinusoidal Signals11

2-3.1 Relation of Frequency to Period12

2-3.2 Phase Shift and Time Shift13

2-4 Sampling and Plotting Sinusoids15

2-5.1 Review of Complex Numbers17

2-5 Complex Exponentials and Phasors17

2-5.2 Complex Exponential Signals18

2-5.3 The Rotating Phasor Interpretation19

2-5.4 Inverse Euler Formulas21

2-6 Phasor Addition22

2-6.1 Addition of Complex Numbers23

2-6.2 Phasor Addition Rule23

2-6.3 Phasor Addition Rule:Example24

2-6.4 MATLAB Demo of Phasors25

2-6.5 Summary of the Phasor Addition Rule26

2-7 Physics of the Tuning Fork27

2-7.1 Equations from Laws of Physics27

2-7.2 General Solution to the Differential Equation29

2-7.3 Listening to Tones29

2-8 Time Signals:More Than Formulas29

2-9 Summary and Links30

2-10 Problems31

3 Spectrum Representation36

3-1 The Spectrum of a Sum of Sinusoids36

3-1.1 Notation Change38

3-1.2 Graphical Plot of the Spectrum38

3-2 Beat Notes39

3-2.1 Multiplication of Sinusoids39

3-2.2 Beat Note Waveform40

3-2.3 Amplitude Modulation41

3-3 Periodic Waveforms43

3-3.1 Synthetic Vowel44

3-3.2 Example of a Nonperiodic Signal45

3-4 Fourier Series47

3-4.2 Fourier Series Derivation48

3-4.1 Fourier Series:Analysis48

3-5 Spectrum of the Fourier Series50

3-6 Fourier Analysis of Periodic Signals51

3-6.1 The Square Wave52

3-6.1.1 DC Value of a Square Wave53

3-6.2 Spectrum for a Square Wave53

3-6.3 Synthesis of a Square Wave54

3-6.4 Triangle Wave55

3-6.5 Synthesis of a Triangle Wave56

3-6.6 Convergence of Fourier Synthesis57

3-7 Time-Frequency Spectrum57

3-7.1 Stepped Frequency59

3-7.2 Spectrogram Analysis59

3-8.1 Chirp or Linearly Swept Frequency60

3-8 Frequency Modulation:Chirp Signals60

3-8.2 A Closer Look at Instantaneous Frequency62

3-9 Summary and Links63

3-10 Problems64

4 Sampling and Aliasing71

4-1 Sampling71

4-1.1 Sampling Sinusoidal Signals73

4-1.2 The Concept of Aliasing75

4-1.3 Spectrum of a Discrete-Time Signal76

4-1.4 The Sampling Theorem77

4-1.5 Ideal Reconstruction78

4-2 Spectrum View of Sampling and Reconstruction79

4-2.1 Spectrum of a Discrete-Time Signal Obtained by Sampling79

4-2.2 Over-Sampling79

4-2.3 Aliasing Due to Under-Sampling81

4-2.4 Folding Due to Under-Sampling82

4-2.5 Maximum Reconstructed Frequency83

4-3 Strobe Demonstration84

4-3.1 Spectrum Interpretation87

4-4 Discrete-to-Continuous Conversion88

4-4.1 Interpolation with Pulses88

4-4.2 Zero-Order Hold Interpolation89

4-4.3 Linear Interpolation90

4-4.4 Cubic Spline Interpolation90

4-4.5 Over-Sampling Aids Interpolation91

4-4.6 Ideal Bandlimited Interpolation92

4-5 The Sampling Theorem93

4-6 Summary and Links94

4-7 Problems96

5 FIR Filters101

5-1 Discrete-Time Systems102

5-2 The Running-Average Filter102

5-3 The General FIR Filter105

5-3.1 An Illustration of FIR Filtering106

5-3.2 The Unit Impulse Response107

5-3.2.1 Unit Impulse Sequence107

5-3.2.2 Unit Impulse Response Sequence108

5-3.2.3 The Unit-Delay System109

5-3.3 Convolution and FIR Filters110

5-3.3.1 Computing the Output of a Convolution110

5-4 Implementation of FIR Filters111

5-4.1 Building Blocks111

5-3.3.2 Convolution in MATLAB111

5-4.1.1 Multiplier112

5-4.1.2 Adder112

5-4.1.3 Unit Delay112

5-4.2 Block Diagrams113

5-4.2.1 Other Block Diagrams113

5-4.2.2 Internal Hardware Details115

5-5 Linear Time-Invariant(LTI)Systems115

5-5.1 Time Invariance116

5-5.2 Linearity117

5-5.3 The FIR Case117

5-6 Convolution and LTI Systems118

5-6.1 Derivation of the Convolution Sum118

5-6.2 Some Properties of LTI Systems120

5-6.2.3 Associative Property of Convolution121

5-6.2.1 Convolution as an Operator121

5-6.2.2 Commutative Property of Convolution121

5-7 Cascaded LTI Systems122

5-8 Example of FIR Filtering124

5-9 Summary and Links126

5-10 Problems126

6 Frequency Response of FIR Filters130

6-1 Sinusoidal Response of FIR Systems130

6-2 Superposition and the Frequency Response132

6-3 Steady-State and Transient Response135

6-4 Properties of the Frequency Response137

6-4.1 Relation to Impulse Response and Difference Equation137

6-4.2 Periodicity of H(ej?)138

6-4.3 Conjugate Symmetry138

6-5.1 Delay System139

6-5 Graphical Representation of the Frequency Response139

6-5.2 First-Difference System140

6-5.3 A Simple Lowpass Filter142

6-6 Cascaded LTI Systems143

6-7 Running-Average Filtering145

6-7.1 Plotting the Frequency Response146

6-7.2 Cascade of Magnitude and Phase148

6-7.3 Experiment:Smoothing an Image149

6-8 Filtering Sampled Continuous-Time Signals151

6-8.1 Example:Lowpass Averager152

6-8.2 Interpretation of Delay154

6-9 Summary and Links155

6-10 Problems157

7 z-Transforms163

7-1 Definition of the z-Transform164

7-2 The z-Transform and Linear Systems165

7-2.1 The z-Transform of an FIR Filter166

7-3 Properties of the z-Transform167

7-3.1 The Superposition Property of the z-Transform168

7-3.2 The Time-Delay Property of the z-Transform168

7-3.3 A General z-Transform Formula169

7-4 The z-Transform as an Operator169

7-4.1 Unit-Delay Operator169

7-4.2 Operator Notation170

7-4.3 Operator Notation in Block Diagrams170

7-5 Convolution and the z-Transform171

7-5.1 Cascading Systems173

7-5.2 Factoring z-Polynomials174

7-5.3 Deconvolution175

7-6 Relationship Between the z-Domain and the ?-Domain175

7-6.1 The z-Plane and the Unit Circle176

7-6.2 The Zeros and Poles of H(z)177

7-6.3 Significance of the Zeros of H(z)178

7-6.4 Nulling Filters179

7-6.5 Graphical Relation Between z and ?180

7-7 Useful Filters181

7-7.1 The L-Point Running-Sum Filter181

7-7.2 A Complex Bandpass Filter183

7-7.3 A Bandpass Filter with Real Coefficients185

7-8 Practical Bandpass Filter Design186

7-9.2 Locations of the Zeros of FIR Linear-Phase Systems189

7-9.1 The Linear-Phase Condition189

7-9 Properties of Linear-Phase Filters189

7-10 Summary and Links190

7-11 Problems191

8 IIR Filters196

8-1 The General IIR Difference Equation197

8-2 Time-Domain Response198

8-2.1 Linearity and Time Invariance of IIR Filters199

8-2.2 Impulse Response of a First-Order IIR System200

8-2.3 Response to Finite-Length Inputs201

8-2.4 Step Response of a First-Order Recursive System202

8-3 System Function of an IIR Filter204

8-3.1 The General First-Order Case205

8-3.2.1 Direct Form Ⅰ Structure206

8-3.2 The System Function and Block-Diagram Structures206

8-3.2.2 Direct Form Ⅱ Structure207

8-3.2.3 The Transposed Form Structure208

8-3.3 Relation to the Impulse Response209

8-3.4 Summary of the Method209

8-4 Poles and Zeros210

8-4.1 Poles or Zeros at the Origin or Infinity211

8-4.2 Pole Locations and Stability211

8-5 Frequency Response of an IIR Filter212

8-5.1 Frequency Response using MATLAB213

8-5.2 Three-Dimensional Plot of a System Function214

8-6 Three Domains216

8-7 The Inverse z-Transform and Some Applications216

8-7.1 Revisiting the Step Response of a First-Order System217

8-7.2 A General Procedure for Inverse z-Transformation218

8-8 Steady-State Response and Stability220

8-9 Second-Order Filters223

8-9.1 z-Transform of Second-Order Filters223

8-9.2 Structures for Second-Order IIR Systems224

8-9.3 Poles and Zeros225

8-9.4 Impulse Response of a Second-Order IIR System226

8-9.4.1 Real Poles227

8-9.5 Complex Poles228

8-10 Frequency Response of Second-Order IIR Filter231

8-10.1 Frequency Response via MATLAB232

8-10.2 3-dB Bandwidth232

8-10.3 Three-Dimensional Plot of System Functions233

8-11 Example of an IIR Lowpass Filter236

8-12 Summary and Links237

8-13 Problems238

9 Continuous-Time Signals and LTI Systems245

9-1 Continuous-Time Signals246

9-1.1 Two-Sided Infinite-Length Signals246

9-1.2 One-Sided Signals247

9-1.3 Finite-Length Signals248

9-2 The Unit Impulse248

9-2.1 Sampling Property of the Impulse250

9-2.2 Mathematical Rigor252

9-2.3 Engineering Reality252

9-2.4 Derivative of the Unit Step252

9-3 Continuous-Time Systems254

9-3.1 Some Basic Continuous-Time Systems254

9-4 Linear Time-Invariant Systems255

9-3.3 Analogous Discrete-Time Systems255

9-3.2 Continuous-Time Outputs255

9-4.1 Time-Invariance256

9-4.2 Linearity256

9-4.3 The Convolution Integral257

9-4.4 Properties of Convolution259

9-5 Impulse Responses of Basic LTI Systems260

9-5.1 Integrator260

9-5.2 Differentiator261

9-5.3 Ideal Delay261

9-6 Convolution of Impulses261

9-7 Evaluating Convolution Integrals263

9-7.1 Delayed Unit-Step Input263

9-7.2 Evaluation of Discrete Convolution267

9-7.3 Square-Pulse Input268

9-7.4 Very Narrow Square Pulse Input269

9-7.5 Discussion of Convolution Examples270

9-8 Properties of LTI Systems270

9-8.1 Cascade and Parallel Combinations270

9-8.2 Differentiation and Integration of Convolution272

9-8.3 Stability and Causality273

9-9 Using Convolution to Remove Multipath Distortion276

9-10 Summary278

9-11 Problems279

10 Frequency Response285

10-1 The Frequency Response Function for LTI Systems285

10-1.1 Plotting the Frequency Response287

10-1.2 Magnitude and Phase Changes288

10-1.1.1 Logarithmic Plot288

10-2 Response to Real Sinusoidal Signals289

10-2.1 Cosine Inputs290

10-2.2 Symmetry of H(jω)290

10-2.3 Response to a General Sum of Sinusoids293

10-2.4 Periodic Input Signals294

10-3 Ideal Filters295

10-3.1 Ideal Delay System295

10-3.2 Ideal Lowpass Filter296

10-3.3 Ideal Highpass Filter297

10-3.4 Ideal Bandpass Filter297

10-4 Application of Ideal Filters298

10-5 Time-Domain or Frequency-Domain?300

10-6 Summary/Future301

10-7 Problems302

11 Continuous-Time Fourier Transform307

11-1 Definition of the Fourier Transform308

11-2 Fourier Transform and the Spectrum310

11-2.1 Limit of the Fourier Series310

11-3 Existence and Convergence of the Fourier Transform312

11-4 Examples of Fourier Transform Pairs313

11-4.1 Right-Sided Real Exponential Signals313

11-4.1.1 Bandwidth and Decay Rate314

11-4.2 Rectangular Pulse Signals314

11-4.3 Bandlimited Signals316

11-4.4 Impulse in Time or Frequency317

11-4.5 Sinusoids318

11-4.6 Periodic Signals319

11-5.1 The Scaling Property322

11-5 Properties of Fourier Transform Pairs322

11-5.2 Symmetry Properties of Fourier Transform Pairs324

11-6 The Convolution Property326

11-6.1 Frequency Response326

11-6.2 Fourier Transform of a Convolution327

11-6.3 Examples of the Use of the Convolution Property328

11-6.3.1 Convolution of Two Bandlimited Functions328

11-6.3.2 Product of Two Sinc Functions329

11-6.3.3 Partial Fraction Expansions330

11-7 Basic LTI Systems332

11-7.1 Time Delay332

11-7.2 Differentiation333

11-7.3 Systems Described by Differential Equations334

11-8.1 The General Signal Multiplication Property335

11-8 The Multiplication Property335

11-8.2 The Frequency Shifting Property336

11-9 Table of Fourier Transform Properties and Pairs337

11-10 Using the Fourier Transform for Multipath Analysis337

11-11 Summary341

11-12 Problems342

12 Filtering,Modulation,and Sampling346

12-1 Linear Time-Invariant Systems346

12-1.1 Cascade and Parallel Configurations347

12-1.2 Ideal Delay348

12-1.3 Frequency Selective Filters351

12-1.3.1 Ideal Lowpass Filter351

12-1.3.2 Other Ideal Frequency Selective Filters352

12-1.4 Example of Filtering in the Frequency-Domain353

12-1.5 Compensation for the Effect of an LTI Filter355

12-2 Sinewave Amplitude Modulation358

12-2.1 Double-Sideband Amplitude Modulation358

12-2.2 DSBAM with Transmitted Carrier(DSBAM-TC)362

12-2.3 Frequency Division Multiplexing366

12-3 Sampling and Reconstruction368

12-3.1 The Sampling Theorem and Aliasing368

12-3.2 Bandlimited Signal Reconstruction370

12-3.3 Bandlimited Interpolation372

12-3.4 Ideal C-to-D and D-to-C Converters373

12-3.5 The Discrete-Time Fourier Transform375

12-3.6 The Inverse DTFT376

12-3.7 Discrete-Time Filtering of Continuous-Time Signals377

12-4 Summary380

12-5 Problems381

13 Computing the Spectrum389

13-1 Finite Fourier Sum390

13-2 Too Many Fourier Transforms?391

13-2.1 Relation of the DTFT to the CTFT392

13-2.2 Relation of the DFT to the DTFT393

13-2.3 Relation of the DFT to the CTFT393

13-3 Time-Windowing393

13-4 Analysis of a Sum of Sinusoids395

13-4.1 DTFT of a Windowed Sinusoid398

13-5 Discrete Fourier Transform399

13-5.1 The Inverse DFT400

13-5.2 Summary of the DFT Representation401

13-5.3 The Fast Fourier Transform(FFT)402

13-5.4 Negative Frequencies and the DFT402

13-5.5 DFT Example403

13-6 Spectrum Analysis of Finite-Length Signals405

13-7 Spectrum Analysis of Periodic Signals407

13-8 The Spectrogram408

13-8.1 Spectrogram Display409

13-8.2 Spectrograms in MATLAB410

13-8.3 Spectrogram of a Sampled Periodic Signal410

13-8.4 Resolution of the Spectrogram411

13-8.4.1 Resolution Experiment412

13-8.5 Spectrogram of a Musical Scale413

13-8.6 Spectrogram of a Speech Signal415

13-8.7 Filtered Speech418

13-9 The Fast Fourier Transform(FFT)420

13-9.1 Derivation of the FFT420

13-9.1.1 FFT Operation Count421

13-10 Summary and Links423

13-11 Problems424

A Complex Numbers427

A-1 Introduction428

A-2 Notation for Complex Numbers428

A-2.1 Rectangular Form428

A-2.2 Polar Form429

A-2.3 Conversion:Rectangular and Polar430

A-2.4 Difficulty in Second or Third Quadrant431

A-3 Euler s Formula431

A-3.1 Inverse Euler Formulas432

A-4 Algebraic Rules for Complex Numbers432

A-4.1 Complex Number Exercises434

A-5 Geometric Views of Complex Operations434

A-5.1 Geometric View of Addition435

A-5.2 Geometric View of Subtraction436

A-5.3 Geometric View of Multiplication437

A-5.4 Geometric View of Division437

A-5.5 Geometric View of the Inverse,z-1437

A-5.6 Geometric View of the Conjugate,z＊438

A-6 Powers and Roots438

A-6.1 Roots of Unity439

A-6.1.1 Procedure for Finding Multiple Roots440

A-7 Summary and Links441

A-8 Problems441

B Programming in MATLAB443

B-1 MATLAB Help444

B-2 Matrix Operations and Variables444

B-2.2.1 A Review of Matrix Multiplication445

B-2.1 The Colon Operator445

B-2.2 Matrix and Array Operations445

B-2.2.2 Pointwise Array Operations446

B-3 Plots and Graphics446

B-3.1 Figure Windows447

B-3.2 Multiple Plots447

B-3.3 Printing and Saving Graphics447

B-4 Programming Constructs447

B-4.1 MATLAB Built-in Functions448

B-4.2 Program Flow448

B-5 MATLAB Scripts448

B-6 Writing a MATLAB Function448

B-6.1 Creating A Clip Function449

B-7 Programming Tips451

B-6.2 Debugging a MATLAB M-file451

B-7.2 Repeating Rows or Columns452

B-7.3 Vectorizing Logical Operations452

B-7.1 Avoiding Loops452

B-7.4 Creating an Impulse453

B-7.5 The Find Function453

B-7.6 Seek to Vectorize454

B-7.7 Programming Style454

C Laboratory Projects455

C-1 Introduction to MATLAB457

C-1.1 Pre-Lab457

C-1.1.1 Overview457

C-1.1.2 Movies:MATLAB Tutorials457

C-1.2 Warm-up458

C-1.1.3 Getting Started458

C-1.2.1 MATLAB Array Indexing459

C-1.2.2 MATLAB Script Files459

C-1.2.3 MATLAB Sound(optional)460

C-1.3 Laboratory:Manipulating Sinusoids with MATLAB460

C-1.3.1 Theoretical Calculations461

C-1.3.2 Complex Amplitude461

C-1.4 Lab Review Questions461

C-2 Encoding and Decoding Touch-Tone Signals463

C-2.1 Introduction463

C-2.1.1 Review463

C-2.1.2 Background:Telephone Touch-Tone Dialing463

C-2.2 Pre-Lab464

C-2.2.1 Signal Concatenation464

C-2.1.3 DTMF Decoding464

C-2.2.2 Comment on Efficiency465

C-2.2.3 Encoding from a Table465

C-2.2.4 Overlay Plotting465

C-2.3 Warm-up:DTMF Synthesis465

C-2.3.1 DTMF Dial Function466

C-2.3.2 Simple Bandpass Filter Design467

C-2.4 Lab:DTMF Decoding468

C-2.4.1 Filter Bank Design:dtmfdesign.m468

C-2.4.2 A Scoring Function:dtmfscore.m469

C-2.4.3 DTMF Decode Function:dtmfrun.m470

C-2.4.4 Testing471

C-2.4.5 Telephone Numbers471

C-2.4.6 Demo472

C-3 Two Convolution GUIs473

C-3.1 Introduction473

C-3.2 Pre-Lab:Run the GUIs473

C-3.2.1 Discrete-Time Convolution Demo473

C-3.2.2 Continuous-Time Convolution Demo474

C-3.3 Warm-up:Run the GUIs475

C-3.3.1 Continuous-Time Convolution GUI475

C-3.3.2 Discrete Convolution GUI475

C-3.4 Lab Exercises475

C-3.4.1 Continuous-Time Convolution475

C-3.4.2 Continuous-Time Convolution Again476

C-3.4.3 Discrete-Time Convolution476

D CD-ROM Demos478

Index482