Look-Ahead Based Sigma-Delta Modulation

By: Erwin Janssen, Arthur van Roermund

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Hardcover | 7 April 2011

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Hardcover
260 Pages

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23.5 x 15.24 x 1.91

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The aim of this book is to expand and improve upon the existing knowledge on discrete-time 1-bit look-ahead sigma-delta modulation in general, and to come to a solution for the above mentioned specific issues arising from 1-bit sigma-delta modulation for SA-CD. In order to achieve this objective an analysis is made of the possibilities for improving the performance of digital noise-shaping look-ahead solutions. On the basis of the insights obtained from the analysis, several novel generic 1-bit look-ahead solutions that improve upon the state-of-the-art will be derived and their performance will be evaluated and compared. Finally, all the insights are combined with the knowledge of the SA-CD lossless data compression algorithm to come to a specifically for SA-CD optimized look-ahead design.

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Non-Fiction Mathematics Algebra Engineering & Technology Electronics & Communications Engineering Electronics Engineering Circuits & Components Computing & I.T.Computer Networking & Communications Computer Hardware

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
Table of Contents provided by Ingram. All Rights Reserved.

Look-Ahead Based Sigma-Delta Modulation

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