This book provides a balanced account of analog, digital and mixed-mode signal processing with applications in telecommunications. Part I Perspective gives an overview of the areas of Systems on a Chip (Soc) and mobile communication which are used to demonstrate the complementary relationship between analog and digital systems. Part II Analog (continuous-time) and Digital Signal Processing contains both fundamental and advanced analysis, and design techniques, of analog and digital systems. This includes analog and digital filter design; fast Fourier transform (FFT) algorithms; stochastic signals; linear estimation and adaptive filters. Part III Analog MOS Integrated Circuits for Signal Processing covers basic MOS transistor operation and fabrication through to the design of complex integrated circuits such as high performance Op Amps, Operational Transconductance Amplifiers (OTA's) and Gm-C circuits. Part IV Switched-capacitor and Mixed-mode Signal Processing outlines the design of switched-capacitor filters, and concludes with sigma-delta data converters as an extensive application of analog and digital signal processing · Contains the fundamentals and advanced techniques of continuous-time and discrete-time signal processing. · Presents in detail the design of analog MOS integrated circuits for signal processing, with application to the design of switched-capacitor filters. · Uses the comprehensive design of integrated sigma-delta data converters to illustrate and unify the techniques of signal processing. · Includes solved examples, end of chapter problems and MATLABŪ throughout the book, to help readers understand the mathematical complexities of signal processing. The treatment of the topic is at the senior undergraduate to graduate and professional levels, with sufficient introductory material for the book to be used as a self-contained reference.

**About the Author xv****Preface xvii**

**Part I PERSPECTIVE**

**1 Analog, Digital and Mixed-mode Signal Processing 3**

1.1 Digital Signal Processing 3

1.2 Moore’s Law and the “Cleverness” Factor 3

1.3 System on a Chip 3

1.4 Analog and Mixed-mode Signal Processing 4

1.5 Scope 5

**Part II ANALOG (CONTINUOUS-TIME) AND DIGITAL SIGNAL PROCESSING**

**2 Analog Continuous-time Signals and Systems 9**

2.1 Introduction 9

2.2 The Fourier Series in Signal Analysis and Function Approximation 9

*2.2.1 Definitions* 9

*2.2.2 The Time and Discrete Frequency Domains* 10

*2.2.3 Convolution* 12

*2.2.4 Parseval’s Theorem and Power Spectrum* 12

*2.2.5 The Gibbs’ Phenomenon* 12

*2.2.6 Window Functions* 13

2.3 The Fourier Transformation and Generalized Signals 14

*2.3.1 Definitions and Properties* 14

*2.3.2 Parseval’s Theorem and Energy Spectra* 16

*2.3.3 Correlation Functions* 17

*2.3.4 The Unit Impulse and Generalized Signals* 17

*2.3.5 The Impulse Response and System Function* 18

*2.3.6 Periodic Signals* 19

*2.3.7 The Uncertainty Principle* 19

2.4 The Laplace Transform and Analog Systems 19

*2.4.1 The Complex Frequency* 19

*2.4.2 Properties of the Laplace Transform* 21

*2.4.3 The System Function* 22

2.5 Elementary Signal Processing Building Blocks 24

*2.5.1 Realization of the Elementary Building Blocks using Operational Amplifier Circuits* 24

2.6 Realization of Analog System Functions 29

*2.6.1 General Principles and the Use of Op Amp Circuits* 29

*2.6.2 Realization Using OTAs and Gm* − *C Circuits* 32

2.7 Conclusion 34

Problems 34

**3 Design of Analog Filters 39**

3.1 Introduction 39

3.2 Ideal Filters 39

3.3 Amplitude-oriented Design 43

*3.3.1 Maximally Flat Response in both Pass-band and Stop-band* 44

*3.3.2 Chebyshev Response* 46

*3.3.3 Elliptic Function Response* 48

3.4 Frequency Transformations 49

*3.4.1 Low-pass to Low-pass Transformation* 50

*3.4.2 Low-pass to High-pass Transformation* 50

*3.4.3 Low-pass to Band-pass Transformation* 50

*3.4.4 Low-pass to Band-stop Transformation* 51

3.5 Examples 52

3.6 Phase-oriented Design 54

*3.6.1 Phase and Delay Functions* 54

*3.6.2 Maximally Flat Delay Response* 56

3.7 Passive Filters 58

3.8 Active Filters 59

3.9 Use of MATLAB® for the Design of Analog Filters 62

*3.9.1 Butterworth Filters* 62

*3.9.2 Chebyshev Filters* 63

*3.9.3 Elliptic Filters* 63

*3.9.4 Bessel Filters* 64

3.10 Examples of the use of MATLAB® 65

3.11 A Comprehensive Application: Pulse Shaping for Data Transmission 67

3.12 Conclusion 70

Problems 72

**4 Discrete Signals and Systems 75**

4.1 Introduction 75

4.2 Digitization of Analog Signals 75

*4.2.1 Sampling* 76

*4.2.2 Quantization and Encoding* 84

4.3 Discrete Signals and Systems 85

4.4 Digital Filters 87

4.5 Conclusion 92

Problems 93

**5 Design of Digital Filters 95**

5.1 Introduction 95

5.2 General Considerations 95

5.3 Amplitude-oriented Design of IIR Filters 98

*5.3.1 Low-pass Filters* 98

*5.3.2 High-pass Filters* 105

*5.3.3 Band-pass Filters* 107

*5.3.4 Band-stop Filters* 108

5.4 Phase-oriented Design of IIR Filters 108

*5.4.1 General Considerations* 108

*5.4.2 Maximally Flat Group-delay Response* 109

5.5 FIR Filters 111

*5.5.1 The Exact Linear Phase Property* 111

*5.5.2 Fourier-coefficient Filter Design* 118

*5.5.3 Monotonic Amplitude Response with the Optimum Number of Constraints* 128

*5.5.4 Optimum Equiripple Response in both Passband and Stopband* 128

5.6 Comparison Between IIR and FIR Filters 133

5.7 Use of MATLAB® for the Design of Digital Filters 133

*5.7.1 Butterworth IIR Filters* 134

*5.7.2 Chebyshev IIR Filters* 136

*5.7.3 Elliptic IIR Filters* 138

*5.7.4 Realization of the Filter* 140

*5.7.5 Linear Phase FIR Filters* 140

5.8 A Comprehensive Application: Pulse Shaping for Data Transmission 142

*5.8.1 Optimal Design* 142

*5.8.2 Use of MATLAB*® *for the Design of Data Transmission Filters* 144

5.9 Conclusion 146

Problems 146

**6 The Fast Fourier Transform and its Applications 149**

6.1 Introduction 149

6.2 Periodic Signals 150

6.3 Non-periodic Signals 153

6.4 The Discrete Fourier Transform 157

6.5 The Fast Fourier Transform Algorithms 160

*6.5.1 Decimation-in-time Fast Fourier Transform* 161

*6.5.2 Decimation-in-frequency Fast Fourier Transform* 166

*6.5.3 Radix 4 Fast Fourier Transform* 168

6.6 Properties of the Discrete Fourier Transform 170

*6.6.1 Linearity* 170

*6.6.2 Circular Convolution* 170

*6.6.3 Shifting* 171

*6.6.4 Symmetry and Conjugate Pairs* 172

*6.6.5 Parseval’s Relation and Power Spectrum* 173

*6.6.6 Circular Correlation* 174

*6.6.7 Relation to the z -transform* 175

6.7 Spectral Analysis Using the FFT 176

*6.7.1 Evaluation of the Fourier Integral* 176

*6.7.2 Evaluation of the Fourier Coefficients* 178

6.8 Spectral Windows 180

*6.8.1 Continuous-time Signals* 180

*6.8.2 Discrete-time Signals* 184

6.9 Fast Convolution, Filtering and Correlation Using the FFT 184

*6.9.1 Circular (Periodic) Convolution* 184

*6.9.2 Non-periodic Convolution* 185

*6.9.3 Filtering and Sectioned Convolution* 185

*6.9.4 Fast Correlation* 188

6.10 Use of MATLAB® 190

6.11 Conclusion 190

Problems 190

**7 Stochastic Signals and Power Spectra 193**

7.1 Introduction 193

7.2 Random Variables 193

*7.2.1 Probability Distribution Function* 193

*7.2.2 Probability Density Function* 194

*7.2.3 Joint Distributions* 195

*7.2.4 Statistical Parameters* 195

7.3 Analog Stochastic Processes 198

*7.3.1 Statistics of Stochastic Processes* 198

*7.3.2 Stationary Processes* 200

*7.3.3 Time Averages* 201

*7.3.4 Ergodicity* 201

*7.3.5 Power Spectra of Stochastic Signals* 203

*7.3.6 Signals through Linear Systems* 207

7.4 Discrete-time Stochastic Processes 209

*7.4.1 Statistical Parameters* 209

*7.4.2 Stationary Processes* 209

7.5 Power Spectrum Estimation 213

*7.5.1 Continuous-time Signals* 213

*7.5.2 Discrete-time Signals* 216

7.6 Conclusion 217

Problems 217

**8 Finite Word-length Effects in Digital Signal Processors 219**

8.1 Introduction 219

8.2 Input Signal Quantization Errors 221

8.3 Coefficient Quantization Effects 225

8.4 Effect of Round-off Accumulation 227

*8.4.1 Round-off Accumulation without Coefficient Quantization* 228

*8.4.2 Round-off Accumulation with Coefficient Quantization* 235

8.5 Auto-oscillations: Overflow and Limit Cycles 238

*8.5.1 Overflow Oscillations* 238

*8.5.2 Limit Cycles and the Dead-band Effect* 241

8.6 Conclusion 244

Problems 244

**9 Linear Estimation, System Modelling and Adaptive Filters 245**

9.1 Introduction 245

9.2 Mean-square Approximation 245

*9.2.1 Analog Signals* 245

*9.2.2 Discrete Signals* 247

9.3 Linear Estimation, Modelling and Optimum Filters 248

9.4 Optimum Minimum Mean-square Error Analog Estimation 250

*9.4.1 Smoothing by Non-causal Wiener Filters* 250

*9.4.2 Causal Wiener Filters* 253

9.5 The Matched Filter 253

9.6 Discrete-time Linear Estimation 255

*9.6.1 Non-recursive Wiener Filtering* 256

*9.6.2 Adaptive Filtering Using the Minimum Mean Square Error Gradient Algorithm* 260

*9.6.3 The Least Mean Square Error Gradient Algorithm* 263

9.7 Adaptive IIR Filtering and System Modelling 263

9.8 An Application of Adaptive Filters: Echo Cancellers for Satellite Transmission of Speech Signals 266

9.9 Conclusion 267

**Part III ANALOG MOS INTEGRATED CIRCUITS FOR SIGNAL PROCESSING**

**10 MOS Transistor Operation and Integrated Circuit Fabrication 271**

10.1 Introduction 271

10.2 The MOS Transistor 271

*10.2.1 Operation* 272

*10.2.2 The Transconductance* 276

*10.2.3 Channel Length Modulation* 278

*10.2.4 PMOS Transistors and CMOS Circuits* 279

*10.2.5 The Depletion-type MOSFET* 280

10.3 Integrated Circuit Fabrication 280

*10.3.1 Wafer Preparation* 281

*10.3.2 Diffusion and Ion Implantation* 281

*10.3.3 Oxidation* 283

*10.3.4 Photolithography* 285

*10.3.5 Chemical Vapour Deposition* 286

*10.3.6 Metallization* 287

*10.3.7 MOSFET Processing Steps* 287

10.4 Layout and Area Considerations for IC MOSFETs 288

10.5 Noise In MOSFETs 290

*10.5.1 Shot Noise* 290

*10.5.2 Thermal Noise* 290

*10.5.3 Flicker (1/f) Noise* 290

*10.5.4 Modelling of Noise* 290

Problems 291

**11 Basic Integrated Circuits Building Blocks 293**

11.1 Introduction 293

11.2 MOS Active Resistors and Load Devices 293

11.3 MOS Amplifiers 295

*11.3.1 NMOS Amplifier with Enhancement Load* 295

*11.3.2 Effect of the Substrate* 296

*11.3.3 NMOS Amplifier with Depletion Load* 297

*11.3.4 The Source Follower* 298

11.4 High Frequency Considerations 300

*11.4.1 Parasitic Capacitances* 300

*11.4.2 The Cascode Amplifier* 303

11.5 The Current Mirror 304

11.6 The CMOS Amplifier 305

11.7 Conclusion 308

Problems 308

**12 Two-stage CMOS Operational Amplifiers 311**

12.1 Introduction 311

12.2 Op Amp Performance Parameters 311

12.3 Feedback Amplifier Fundamentals 314

12.4 The CMOS Differential Amplifier 316

12.5 The Two-stage CMOS Op Amp 321

*12.5.1 The dc Voltage Gain* 322

*12.5.2 The Frequency Response* 322

*12.5.3 The Nulling Resistor* 323

*12.5.4 The Slew Rate and Settling Time* 325

*12.5.5 The Input Common-mode Range and CMRR* 325

*12.5.6 Summary of the Two-stage CMOS Op Amp Design Calculations* 327

12.6 A Complete Design Example 329

12.7 Practical Considerations and Other Non-ideal Effects in Operational Amplifier Design 332

*12.7.1 Power Supply Rejection* 332

*12.7.2 dc Offset Voltage* 332

*12.7.3 Noise Performance* 332

12.8 Conclusion 334

Problems 334

**13 High Performance CMOS Operational Amplifiers and Operational Transconductance Amplifiers 337**

13.1 Introduction 337

13.2 Cascode CMOS Op Amps 337

13.3 The Folded Cascode Op Amp 338

13.4 Low-noise Operational Amplifiers 340

*13.4.1 Low-noise Design by Control of Device Geometries* 340

*13.4.2 Noise Reduction by Correlated Double Sampling* 342

*13.4.3 Chopper-stabilized Operational Amplifiers* 342

13.5 High-frequency Operational Amplifiers 344

*13.5.1 Settling Time Considerations* 345

13.6 Fully Differential Balanced Topology 346

13.7 Operational Transconductance Amplifiers 353

13.8 Conclusion 353

Problems 354

**14 Capacitors, Switches and the Occasional Passive Resistor 357**

14.1 Introduction 357

14.2 MOS Capacitors 357

*14.2.1 Capacitor Structures* 357

*14.2.2 Parasitic Capacitances* 358

*14.2.3 Capacitor-ratio Errors* 358

14.3 The MOS Switch 362

*14.3.1 A Simple Switch* 362

*14.3.2 Clock Feed-through* 362

*14.3.3 The CMOS Switch: Transmission Gate* 364

14.4 MOS Passive Resistors 366

14.5 Conclusion 366

**Part IV SWITCHED-CAPACITOR AND MIXED-MODE SIGNAL PROCESSING**

**15 Design of Microelectronic Switched-capacitor Filters 369**

15.1 Introduction 369

15.2 Sampled and Held Signals 371

15.3 Amplitude-oriented Filters of the Lossless Discrete Integrator Type 374

*15.3.1 The State-variable Ladder Filter* 374

*15.3.2 Strays-insensitive LDI Ladders* 381

*15.3.3 An Approximate Design Technique* 384

15.4 Filters Derived from Passive Lumped Prototypes 388

15.5 Cascade Design 396

15.6 Applications in Telecommunications: Speech Codecs and Data Modems 399

*15.6.1 CODECs* 399

*15.6.2 Data Modems* 399

15.7 Conclusion 400

Problems 400

**16 Non-ideal Effects and Practical Considerations in Microelectronic Switched-capacitor Filters 403**

16.1 Introduction 403

16.2 Effect of Finite Op Amp Gain 403

16.3 Effect of Finite Bandwidth and Slew Rate of Op Amps 405

16.4 Effect of Finite Op Amp Output Resistance 405

16.5 Scaling for Maximum Dynamic Range 405

16.6 Scaling for Minimum Capacitance 407

16.7 Fully Differential Balanced Designs 407

16.8 More on Parasitic Capacitances and Switch Noise 410

16.9 Pre-filtering and Post-filtering Requirements 412

16.10 Programmable Filters 413

16.11 Layout Considerations 415

16.12 Conclusion 416

**17 Integrated Sigma-Delta Data Converters: Extension and Comprehensive Application of Analog and Digital Signal Processing 417**

17.1 Motivation and General Considerations 417

17.2 The First-order Converter 419

17.3 The Second-order Converter 423

17.4 Decimation and Digital Filtering 426

*17.4.1 Principles* 426

*17.4.2 Decimator Structures* 429

17.5 Simulation and Performance Evaluation 433

17.6 A Case Study: Fourth-order Converter 435

17.7 Conclusion 438

**Answers to Selected Problems 439**

**References 445**

**Index 447**