## Description

## Table of Contents

Preface xiii

Acknowledgments xxi

About the Author xxiii

**Chapter 1: Review of Digital Frequency 1**

1.1 Definitions 2

1.2 Defining Digital Frequencies 2

1.3 Mathematical Representation of Digital Frequencies 9

1.4 Normalized Frequency 12

1.5 Representation of Digital Frequencies 13

**Chapter 2: Review of Complex Variables 15**

2.1 Cartesian Form of Complex Numbers 17

2.2 Polar Form of Complex Numbers 21

2.3 Roots of Complex Numbers 27

2.4 Absolute Value of Complex Numbers 35

2.5 Exponential Form of Complex Numbers 36

2.6 Graphs of the Complex Variable *z *38

2.7 Limits 40

2.8 Analytic Functions 41

2.9 Singularity 42

2.10 Entire Functions 42

2.11 The Complex Number 42

2.12 Complex Differentiation 43

2.13 Cauchy-Riemann Equations 47

2.14 Simply Connected Region 51

2.15 Contours 51

2.16 Line Integrals 52

2.17 Real Line Integrals 54

2.18 Complex Line Integrals 84

2.19 Cauchy’s Theorem 96

2.20 Table of Common Integrals 109

2.21 Cauchy’s Integral 109

2.22 Residue Theory 120

2.23 References 127

**Chapter 3: Review of the Fourier Transform 129**

3.1 A Brief Review of the Fourier Series 129

3.2 A Brief Review of the Fourier Transform 157

3.3 Review of the Discrete Fourier Transform (DFT) 187

3.4 DFT Processing Gain 254

3.5 Example DFT Signal Processing Application 261

3.6 Discrete Time Fourier Transform (DTFT) 263

3.7 Fast Fourier Transform (FFT) 267

3.8 References 268

**Chapter 4: Review of the Z-Transform 271**

4.1 Complex Number Representation 271

4.2 Mechanics of the Z-Transform 274

4.3 Left-Sided Z-Transform 277

4.4 Right-Sided Z-Transform 278

4.5 Two-Sided Z-Transform 278

4.6 Convergence of the Z-Transform 279

4.7 System Stability 290

4.8 Properties of the Z-Transform 292

4.9 Common Z-Transform Pairs 304

4.10 Inverse Z-Transform 308

4.11 Pole and Zero Standard Form Plug-In Equations 334

4.12 Applications of the Z-Transform 350

4.13 Summary of Useful Equations 380

4.14 References 381

**Chapter 5: Finite Impulse Response Digital Filtering 383**

5.1 Review of Digital FIR Filters 384

5.2 Parks-McClellan Method of FIR Filter Design 392

5.3 PM Implementation of Half Band Filters 425

5.4 References 433

**Chapter 6: Multirate Finite Impulse Response Filter Design 435**

6.1 Poly Phase Filter (PPF) 436

6.2 Half Band Filter 465

6.3 Cascaded Integrator Comb (CIC) Filter 470

6.4 References 531

**Chapter 7: Complex to Real Conversion 533**

7.1 A Typical Digital Signal Processing (DSP) System 534

7.2 Conversion of a Complex Signal to a Real Signal 540

7.3 Complex to Real Simulation Results 560

7.4 Reference 573

**Chapter 8: Digital Frequency Synthesis 575**

8.1 Numerically Controlled Oscillator (NCO) 575

8.2 Enhanced NCO Phase Accumulator 608

8.3 NCO Synthesized Output Frequency Error 613

8.4 Adding a Programmable Phase Offset to the NCO Output 622

8.5 Design of an Industry-Grade NCO 628

8.6 NCO Phase Dither 641

8.7 References 644

**Chapter 9: Signal Tuning 645**

9.1 Continuous Time (Analog) Fourier Transform 647

9.2 Discrete Time (Digital) Fourier Transform 689

9.3 Useful Equations 754

9.4 References 759

**Chapter 10: Elastic Store Memory 761**

10.1 Example Application of an Elastic Store Memory 762

10.2 PCM Multiplexing Hierarchy 763

10.3 DS-1C Multiplexer Design Overview 768

10.4 Design of the Elastic Store Memory 774

10.5 Hardware Implementation of the Elastic Store Memory 792

10.6 Overall DS-1C Multiplexer Design Block Diagram 801

10.7 Additional Information 803

10.8 References 805

**Chapter 11: Digital Data Locked Loops 807**

11.1 Digital Data Locked Design 808

11.2 Digital Data Locked Steady State Behavior 829

11.3 Digital Data Locked Transient Behavior 834

11.4 Data Locked Loop Bit-Level Simulation 845

11.5 Engineering Note 869

11.6 Summary of Useful Equations 869

11.7 References 871

**Chapter 12: Channelized Filter Bank 873**

12.1 Introductory Description 873

12.2 Channelizer Functional Overview 877

12.3 Channelizer Detailed Design Concepts 919

12.4 Channelizer Software Simulation Results 962

12.5 Channelizer Hardware Design Example 967

12.6 Summary of Useful Equations 974

12.7 References 975

**Chapter 13: Digital Automatic Gain Control 977**

13.1 Design of a Type I RMS AGC Circuit 981

13.2 Design of a Type II RMS AGC Circuit 1044

13.3 References 1047

**Appendix A: Mixed Language C/C++ FORTRAN Programming 1049**

A.1 Writing a C/C++ Main Program 1051

A.2 Calling Subroutines and Functions from a C/C++ Main 1051

A.3 Writing a FORTRAN Subroutine 1054

A.4 Writing a FORTRAN Function 1055

A.5 Passing Integer Arguments 1055

A.6 Passing Floating Point Arguments 1057

A.7 Passing Array Arguments 1059

A.8 Passing Pointer Arguments 1060

A.9 Compile/Link Mixed Language C/C++ FORTRAN Programs 1063

A.10 Parks-McClellan FORTRAN Subroutine Called from C Main 1064

A.11 References 1091

*Index 1093*

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