Sigma Delta Modulators - Avideh Zakhor

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Résumé :
Analog-to-digital (A/D) converters are key components in digital signal processing (DSP) systems and are therefore receiving much attention as DSP becomes increasingly prevalent in telephony, audio, video, consumer products, etc. The varying demands on conversion rate, resolution and other characteristics have inspired a large number of competing A/D conversion techniques. Sigma Delta Modulators: Nonlinear Decoding Algorithms and Stability Analysis is concerned with the particular class of A/D techniques called oversampled noise-shaping (ONS) that has recently come into prominence for a number of applications. The popularity of ONS converters is due to their ease of implementation and robustness to circuit imperfectors. An ONS converter consists of an encoder that generates a high-rate, low-resolution digital signal, and a decoder that produces a low-rate, high-resolution digital approximation to the analog encoder input. The conventional decoding approach is based on linear filtering. Sigma Delta Modulators presents the optimal design of an ONS decoder for a given encoder. It is shown that nonlinear decoding can achieve gains in signaling ratio and the encoder architecture. The book then addresses the instability problem that plagues higher-order ONS encoders. A new stability concept is introduced that is well-suited to ONS encoders, and it is applied to the double-loop encoder as well as to the class of interpolative encoders. It is shown that there exists a trade-off between stability and SNR performance. Based on the results, explicit design examples are presented. Sigma Delta Modulators: Nonlinear Decoding Algorithms and Stability Analysis is a valuable reference source for researchers and engineers in industry and academia working on or interested in design and analysis of A/D converters, particularly to those working in quantization theory and signal reconstruction, and can serve as a text for advanced courses on the subjects treated.

Sommaire:
1 Introduction.- 1.1 Analog-to-Digital Conversion.- 1.2 Conventional Conversion.- 1.3 Oversampled Noise-Shaping Conversion.- 1.4 Contributions and Outline of Work.- 2 Properties of ONS Converters with Constant Inputs.- 2.1 Introduction.- 2.2 Single-Loop Encoder.- 2.3 Double-Loop Encoder.- 2.4 A Modified Cascade Structure for Constant Inputs.- 2.5 Summary.- 3 Optimal Decoding for ONS Encoders with Constant Inputs.- 3.1 Introduction.- 3.2 Optimal Decoding under Ideal Conditions.- 3.3 Decoding in the Presence of Non-Idealities.- 3.4 Summary.- 4 An SVD-Based Method for Band-Limiting Finite Extent Signals.- 4.1 Introduction.- 4.2 SVD-Based Band Limitation.- 4.3 Implementation of the SVD.- 4.4 Computational Properties of Band Limitation Methods.- 4.5 Results.- 4.6 Summary.- 5 Optimal Decoding for ONS Decoders with Band-Limited Inputs.- 5.1 Introduction.- 5.2 Reconstruction Algorithm.- 5.3 Results.- 5.4 Decoding in the Presence of Non-Idealities.- 5.5 Summary.- 6 Halftone to Continuous-Tone Conversion of Error-Diffusion Coded Images.- 6.1 Introduction.- 6.2 Error Diffusion Coding.- 6.3 Decoding Algorithm.- 6.4 Results.- 6.5 Summary.- 7 Stability of ONS Encoders.- 7.1 Introduction.- 7.2 Framework for Stability Analysis.- 7.3 Double-Loop Encoder.- 7.4 Interpolative Encoder.- 7.5 Summary.- 8 Conclusions.- 8.1 Summary.- 8.2 Extensions.- 8.3 Future Directions.- A Appendix to Chapter 2.- A.1 Derivations for Single-Loop Encoder.- A.2 Derivations for Double-Loop Encoder.- A.3 Proofs of Theorems.- B Appendix to Chapter 3.- B.1 Performance Measures.- B.2 Only Codewords Yield Compatible Bounds.- B.3 Form of Non-Idealities.- C Appendix to Chapter 4.- C.1 Energy Concentration.- C.2 Resolution of the DFT.- C.3 Effect of Windowing.- D Appendix to Chapter 5.- D.1 Quadratic Programming Approximation.- E Appendix to Chapter 6.- E.1 Stability of Error Diffusion Encoders.- E.2 Two-Dimensional SVD Band Limitation.- F Appendix to Chapter 7.- F.1 Upper Bounds on Double-Loop Limit Cycles.- F.2 Design of Double-Loop Encoder.- F.3 Describing Function Method.- F.4 Proofs of Statements in Section 7.5.2.2.