SIGNAL PROCESSING AND INTEGRATED CIRCUITS ‘The scribes full of wisdom, Their names will last forever. They leave for an inheritance, Their teachings and their books. Their teachings are their Pyramids, Their magical power touches all those who read their writings.’ Egyptian Hieratic Papyrus in the British Museum ‘Theinstinctofconstructiveness,whichisoneofthechiefincentivestoartistic creation, can find in scientific systems a satisfaction more massive than any epic poem. Disinterested curiosity, which is the essence of almost all intellec- tual effort, finds with astonished delight that science can unveil secrets which mightwellhaveseemedforeverundiscoverable...Alifedevotedtoscienceis therefore a happy life, and its happiness is derived from the very best sources that are open to dwellers on this troubled and passionate planet.’ Bertrand Russell ‘The Place of Science in a Liberal Education’ SIGNAL PROCESSING AND INTEGRATED CIRCUITS Hussein Baher ProfessorEmeritusofElectronicEngineering AlexandriaInstituteofEngineeringandTechnology,Egypt A John Wiley & Sons, Ltd., Publication Thiseditionfirstpublished2012 ©2012,JohnWiley&Sons,Ltd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissionto reusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. 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Signalprocessingandintegratedcircuits/HusseinBaher. p.cm. Includesbibliographicalreferencesandindex. ISBN978-0-470-71026-5(cloth) 1.Signalprocessing–Equipmentandsupplies.2.Signal processing–Mathematics.3.Integratedcircuits–Designandconstruction. 4.Electricfilters.I.Title. TK5102.9.B3532012 621.382(cid:2)2–dc23 2011053421 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:9780470710265 Setin10/12ptTimesbyLaserwordsPrivateLimited,Chennai,India Contents 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 viii Contents 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 G −C Circuits 32 m 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 Contents ix 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 x Contents 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 Contents xi 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