Ebook: Look-Ahead Based Sigma-Delta Modulation

High resolution analog-to-digital conversion and digital-to-analog conversion is often realized with the use of a Sigma-Delta Modulator (SDM). The sigma-delta modulation process, although very non-linear when a 1-bit quantizer is used, is nowadays well understood and can be made to deliver a very high signal conversion quality. An example system that pushes the traditional sigma-delta modulation algorithm to its performance limit is the Super Audio CD (SA-CD) standard, in which a 64 times oversampled 1-bit signal is used to represent audio content with an SNR of up to 120~dB over 20~kHz bandwidth. Look-Ahead Based Sigma-Delta Modulation presents a number of alternative digital sigma-delta modulation techniques that make use of look-ahead, a process that takes into account the effect of decisions on the future, to realize an even higher conversion quality than possible with traditional sigma-delta modulation. This book provides the reader with a clear overview of various encoding techniques and demonstrates the improvements in signal conversion quality that can be obtained from their use. Starting from the basic full look-ahead approach that requires several orders of magnitude more computational power than a normal SDM, more efficient structures are derived that are able to realize a far higher signal conversion performance at a fraction of the computational cost. In addition to this, a modulator is derived that is able to generate bitstreams that are optimized for SA-CD usage, i.e. a high signal conversion quality combined with minimal signal entropy. All the look-ahead algorithms presented in this book are described in pseudocode and ample simulation results are provided to judge the effects on the signal conversion performance.;1. Introduction -- 2. Basics of sigma-delta modulation -- 3. Transient SDM performance -- 4. Noise-shaping quantizer model -- 5. Look-ahead sigma-delta modulation -- 6. Reducing the complexity of LA DD conversion -- 7. Trellis sigma-delta modulation -- 8. Efficient Trellis sigma-delta modulation -- 9. Pruned Tree sigma-delta modulation -- 10. Pruned Tree sigma-delta modulation for SA-CD -- 11. Comparison of look-ahead SDM techniques -- 12. Maximum SNR analysis -- 13. General Conclusions -- Appendix A: FFT calculations -- coherent and power averaging -- Appendix B: Descriptions of the used Sigma-Delta Modulators.