| Introduction | p. 1 |
| Basics of Sigma-Delta Modulation | p. 5 |
| AD, DD, and DA Sigma-Delta Conversion | p. 8 |
| AD Conversion | p. 8 |
| DD Conversion | p. 9 |
| DA Conversion | p. 9 |
| Sigma-Delta Structures | p. 10 |
| Linear Modeling of an SDM | p. 12 |
| Sigma-Delta Modulator Performance Indicators | p. 17 |
| Generic Converter Performance | p. 17 |
| SDM Specific Functional Performance | p. 22 |
| SDM Specific Implementation Costs | p. 26 |
| Figure-of-Merit of an SDM | p. 27 |
| Transient SDM Performance | p. 29 |
| Measuring Signal Conversion Quality | p. 29 |
| Steady-State | p. 29 |
| Non-steady-State | p. 30 |
| Time Domain SINAD Measurement | p. 31 |
| Steady-State SINAD Measurement Analysis | p. 33 |
| Obtaining the Linearized STF | p. 34 |
| Time Domain SINAD Measurement | p. 37 |
| Non-steady-State SINAD Measurement Analysis | p. 37 |
| Conclusions | p. 40 |
| Noise-Shaping Quantizer Model | p. 43 |
| Generic Quantizer | p. 43 |
| Noise-Shaping Quantizer | p. 44 |
| Noise-Shaping Quantizer with Multiple Cost Functions | p. 46 |
| Specific Realization Structures | p. 47 |
| Look-Ahead Sigma-Delta Modulation | p. 49 |
| Noise-Shaping Quantizer with Look-Ahead | p. 49 |
| Look-Ahead Enabled SDM Model | p. 51 |
| Look-Ahead Principle | p. 52 |
| Quantizer Cost Function | p. 54 |
| Obtaining Information About the Future | p. 55 |
| Approximated Future Input | p. 55 |
| Actual Future Input | p. 56 |
| Full Look-Ahead Algorithm | p. 56 |
| Linear Modeling of a Look-Ahead SDM | p. 59 |
| Boundary Conditions and Assumptions | p. 59 |
| Feed-Forward Look-Ahead SDM | p. 60 |
| Feed-Back Look-Ahead SDM | p. 62 |
| Benefits and Disadvantages of Look-Ahead | p. 64 |
| Benefits | p. 65 |
| Disadvantages | p. 67 |
| Look-Ahead AD Conversion | p. 68 |
| Potential Benefits and Disadvantages of Look-Ahead in AD Conversion | p. 68 |
| Feasibility of a Look-Ahead ADC | p. 69 |
| Hybrid Look-Ahead ADC | p. 71 |
| Conclusion | p. 72 |
| Look-Ahead DD Conversion | p. 72 |
| Conclusions | p. 75 |
| Reducing the Computational Complexity of Look-Ahead DD Conversion | p. 77 |
| Full Look-Ahead | p. 77 |
| Complete Response Calculation with Reuse of Intermediate Results | p. 78 |
| Select and Continue with Half of the Solutions | p. 78 |
| Linear Decomposition of the Filter Response | p. 79 |
| Conditional Computation of the Solutions | p. 80 |
| Calculating Multiple Output Symbols per Step | p. 80 |
| Summary | p. 82 |
| Pruned Look-Ahead | p. 82 |
| Motivation for Pruning | p. 83 |
| Basic Pruned Look-Ahead Modulation | p. 84 |
| Pruned Look-Ahead Modulation with Reuse of Results | p. 86 |
| Summary | p. 95 |
| Pruned Look-Ahead Modulator Realizations | p. 95 |
| Trellis Sigma-Delta Modulation | p. 96 |
| Efficient Trellis Sigma-Delta Modulation | p. 97 |
| Pruned Tree Sigma-Delta Modulation | p. 98 |
| Pruned Tree Sigma-Delta Modulation for SA-CD | p. 100 |
| Conclusions | p. 101 |
| Trellis Sigma-Delta Modulation | p. 103 |
| Algorithm - Kato Model | p. 104 |
| Hidden Markov Model | p. 104 |
| Algorithm Steps | p. 106 |
| Algorithm - Pruned Look-Ahead Model | p. 109 |
| Verification of the Linearized NTF and STF | p. 110 |
| NTF | p. 110 |
| STF | p. 112 |
| Relation Trellis Order and Trellis Depth | p. 113 |
| Simulation Setup | p. 114 |
| Trellis Depth as a Function of the Trellis Order and the Signal Amplitude | p. 114 |
| Trellis Depth as a Function of the Signal Frequency | p. 116 |
| Trellis Depth as a Function of the Loop-Filter Configuration | p. 117 |
| Summary | p. 118 |
| Functional Performance | p. 119 |
| SNR, SINAD, THD and SFDR | p. 119 |
| Converter Stability | p. 124 |
| Noise Modulation | p. 128 |
| Summary | p. 130 |
| Implementation Aspects | p. 131 |
| Required Computational Resources | p. 131 |
| Look-Ahead Filter Unit | p. 132 |
| Output Symbol Selection | p. 134 |
| Conclusions | p. 135 |
| Efficient Trellis Sigma-Delta Modulation | p. 137 |
| Reducing the Number of Parallel Paths | p. 137 |
| Algorithm | p. 140 |
| Relation Between N and M | p. 141 |
| Required History Length | p. 143 |
| Functional Performance | p. 145 |
| SNR, SINAD, THD and SFDR | p. 145 |
| Converter Stability | p. 149 |
| Noise Modulation | p. 150 |
| Summary | p. 152 |
| Implementation Aspects | p. 153 |
| Selection Step | p. 154 |
| Conclusions | p. 156 |
| Pruned Tree Sigma-Delta Modulation | p. 159 |
| Removing the Test for Uniqueness | p. 159 |
| Algorithm | p. 161 |
| Initialization Phase | p. 162 |
| Operation Phase | p. 162 |
| Required History Length | p. 163 |
| Functional Performance | p. 165 |
| SNR, SINAD, THD and SFDR | p. 165 |
| Converter Stability | p. 168 |
| Noise Modulation | p. 170 |
| Summary | p. 172 |
| Implementation Aspects | p. 174 |
| Conclusions | p. 175 |
| Pruned Tree Sigma-Delta Modulation for SA-CD | p. 179 |
| Requirements of an SA-CD Modulator | p. 179 |
| SA-CD Lossless Data Compression | p. 181 |
| Dual Optimization | p. 184 |
| Predictor Cost Function | p. 185 |
| Combining the Cost Functions | p. 187 |
| Spectral Shaping | p. 188 |
| Algorithm | p. 190 |
| Functional Performance | p. 193 |
| Lossless Data Compression | p. 193 |
| SNR, SINAD, THD and SFDR | p. 194 |
| Converter Stability | p. 196 |
| Noise Modulation | p. 197 |
| Summary | p. 200 |
| Implementation Aspects | p. 201 |
| Conclusions | p. 202 |
| Comparison of Look-Ahead SDM Techniques | p. 205 |
| Alternative Look-Ahead Techniques | p. 205 |
| Algorithm Comparison | p. 206 |
| Functional Performance Comparison | p. 209 |
| SNR, SINAD, THD and SFDR | p. 209 |
| Converter Stability | p. 213 |
| Noise Modulation | p. 216 |
| Lossless Data Compression | p. 218 |
| Summary | p. 220 |
| Conclusions | p. 221 |
| Maximum SNR Analysis | p. 225 |
| Experiment 1 | p. 225 |
| Experiment 2 | p. 227 |
| Analysis | p. 228 |
| Second Order Filter Stability | p. 229 |
| High Order Filter Stability | p. 231 |
| Obtaining the Maximum SNR | p. 233 |
| Theoretical Maximum SNR | p. 235 |
| Conclusions | p. 237 |
| General Conclusions | p. 239 |
| FFT Calculations - Coherent and Power Averaging | p. 241 |
| Description of the Used Sigma-Delta Modulators | p. 243 |
| References | p. 245 |
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