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Über dieses Buch

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.



Chapter 1. Introduction

Erwin Janssen, Arthur van Roermund

Chapter 2. Basics of Sigma-Delta Modulation

This chapter provides a basic introduction to sigma-delta modulation in general. It first discusses the use of sigma-delta modulation for analog-to-digital, digital-to-digital, and digital-to-analog conversion, after which the most popular sigma-delta structures are presented. A procedure for basic linear modeling of sigma-delta modulators is presented and it’s shortcomings are demonstrated. Because of the potentially large discrepancy between the by the model predicted results and the actual obtained results, time domain simulations are used in this book. Finally, a number of often used sigma-delta performance indicators are presented to set a basis for the comparison of different sigma-delta modulator realizations.
Erwin Janssen, Arthur van Roermund

Chapter 3. Transient SDM Performance

Virtually all traditional signal quality analysis procedures operate on data in the frequency domain, and therefore require steady-state signals. However, real-life signals are, typically, not steady-state. In order to be able to measure the conversion quality of a sigma-delta modulator under non-steady-state excitation, in this chapter a time domain SINAD measurement method is introduced. The operation of this time domain method is first verified with steady-state signal measurements, and finally applied to non-steady-state signals. The simulations on various non-steady-state signals indicate that no significant conversion errors are generated, and that the traditional signal quality analysis procedures are adequate.
Erwin Janssen, Arthur van Roermund

Chapter 4. Noise-Shaping Quantizer Model

In this chapter an abstract model of a noise-shaping quantizer is derived. A noise-shaping quantizer is a more general description of a sigma-delta modulator, consisting of one or more cost functions and a selection function. The cost function is an indication of the quality of a signal or an encoding solution, and the selection function determines the output symbol. In the case of a normal sigma-delta modulator the cost function is implemented by the loop-filter and the selection function by the quantizer. This generalization of the sigma-delta modulator structure will enable to addition of look-ahead functionality in the next chapter.
Erwin Janssen, Arthur van Roermund

Chapter 5. Look-Ahead Sigma-Delta Modulation

The generic noise-shaping quantizer model from chapter four is modified to support look-ahead, and a hypothetical sigma-delta modulator with look-ahead capability is derived. From here the main principles of look-ahead are explored, including linear modeling of a look-ahead modulator, and an overview of expected benefits and disadvantages of a look-ahead sigma-delta modulator. Although only with an infinite amount of look-ahead the global optimal encoding solution can be found, it is concluded that already with a limited amount of look-ahead an improvement in the signal conversion performance can be obtained. The benefits of look-ahead, primarily an increase of the stability and a reduction of the distortion, are the biggest in the case of a 1-bit converter, since here the quantizer is severely non-linear. Therefore, in the remaining chapters the focus will be primarily on 1-bit converters. The operation of the full look-ahead algorithm, an algorithm that can be found in open literate and that performs an exhaustive search for the best solution within the look-ahead depth, is reviewed. With these insights the feasibility of an analog-to-digital converter with look-ahead is investigated, and it is concluded that the feasibility is low. It is found that in the case of a digital-to-digital converter, in principle, look-ahead can be implemented without major difficulties, but that the traditional full look-ahead approach is not computationally efficient.
Erwin Janssen, Arthur van Roermund

Chapter 6. Reducing the Computational Complexity of Look-Ahead DD Conversion

In this chapter the possibilities for reducing the computational load of look-ahead digital-to-digital conversion are explored. An analysis is made of the opportunities to reduce the number of computations required to perform full look-ahead. For small look-ahead depth it is possible to reduce the number of calculations, but for large look-ahead depths the savings that can be realized are limited, and ultimately the number of computations that are required per output symbol doubles with an increase of the look-ahead depth by one. As an alternative to full look-ahead, the possibilities for performing pruned look-ahead are explored. In this case not the full solution space is explored, but based on heuristics a small subset of all the solutions are investigated. This approach can realize a large reduction of the computational load, while the impact on the signal conversion performance can be made negligible small. Because of the potentially large advantage over full look-ahead, several ideas for realizing pruned look-ahead modulators are presented, that are explored in detail in the next chapters.
Erwin Janssen, Arthur van Roermund

Chapter 7. Trellis Sigma-Delta Modulation

Chapter seven presents a full analysis of the Trellis sigma-delta modulation algorithm. This algorithm is the first pruned look-ahead sigma-delta modulation algorithm found in literature. It is a derivative of the full look-ahead algorithm and uses concepts from Trellis (Viterbi) decoding, hence the name. In the Trellis sigma-delta modulation algorithm, at all times, a total number of 2 N potential solutions (paths) are investigated, of which the most recent N symbols are different for all the solutions. The output symbol of the converter is found by tracing back any of the 2 N paths L time steps. After the algorithm discussion a performance analysis is performed, which shows that the Trellis sigma-delta modulation approach results in a converter that has an improved linearity and better stability than a normal sigma-delta modulator, although the computational load is very high. Suggestions for an efficient implementation of the algorithm are provided as well.
Erwin Janssen, Arthur van Roermund

Chapter 8. Efficient Trellis Sigma-Delta Modulation

In chapter eight, an efficient derivative of the Trellis sigma-delta modulator, called the Efficient Trellis sigma-delta modulator, is introduced. Instead of exploring 2 N solutions in parallel, only M solutions out of the possible 2 N are tracked. This is possible since only a fraction of all the 2 N solutions contributes to the final output. The selection of which paths to keep is based on the accumulated path cost, i.e. paths with a low cost have a large probability to be part of the output and are selected, whereas more expensive paths are rejected. Compared to the Trellis sigma-delta modulation algorithm, the computational load is reduced by several orders of magnitude, while at the same time improvements in the linearity and stability are obtained.
Erwin Janssen, Arthur van Roermund

Chapter 9. Pruned Tree Sigma-Delta Modulation

The Pruned Tree sigma-delta modulation algorithm is a further refinement on the algorithms that are described in the previous chapters. This algorithm is a practical realization of the pruned look-ahead approach as derived in chapter six. A total of M paths are tracked, with no constraints on the solution space coverage imposed. The result of this approach is that a performance level that is slightly better than that of the Efficient Trellis sigma-delta modulation algorithm is realized, at a significantly reduced computational load. In the chapter not only the algorithm is detailed, but also the functional performance is extensively studied and important details for an efficient implementation are discussed.
Erwin Janssen, Arthur van Roermund

Chapter 10. Pruned Tree Sigma-Delta Modulation for SA-CD

In chapter ten, the Pruned Tree sigma-delta modulation algorithm for Super Audio CD (SA-CD) is presented. The algorithm has a better compatibility with Super Audio CD, because it generates bitstreams that result in a high lossless data compression gain. This is achieved by adding a cost function to the look-ahead filter that measures the predictability of the output signal. This addition results in an output bitstream that is of a high signal quality, but that is also very predictable, such that the amount of required disc storage space after lossless data compression reduces. This reduction of the required storage space is of great importance, since it solves potential playback duration issues. The addition of the prediction cost function has only a minimal impact on the SNR, while the distortion and the noise-modulation performance of the converter are strongly reduced, resulting in the ideal sigma-delta converter for high-end audio applications.
Erwin Janssen, Arthur van Roermund

Chapter 11. Comparison of Look-Ahead SDM Techniques

All of the previously discussed look-ahead techniques are compared in chapter eleven. The outcome of this comparison is that the normal Pruned Tree sigma-delta modulation algorithm is the best choice if the converter is not intended for audio applications, since it offers the highest SNR, very good linearity, and the largest stability at the minimal computational cost. In the case of a high-end application for Super Audio CD, the Pruned Tree sigma-delta modulation algorithm for SA-CD is the best choice because of the constant in-band noise-floor and the higher compression gains that are obtained on the output bitstream.
Erwin Janssen, Arthur van Roermund

Chapter 12. Maximum SNR Analysis

In this chapter an investigation is made of the apparent limit on the obtainable SNR of a 1-bit look-ahead sigma-delta modulator. The outcome of this investigation is that there is a point of maximal noise shaping, which depends on the filter order. At the point of maximal noise shaping the system is critically stable, and increasing the corner frequency of the loop filter above this point will not change the noise-shaping characteristics, i.e. the look-ahead system forces the same noise shaping as obtained for the critically stable point. If, instead of increasing the loop-filter corner frequency further, a higher filter order is selected in combination with a lower loop-filter corner frequency, a more aggressive noise shaping can be realized that results in a higher SNR. Since the more aggressive noise shaping causes a reduction of the stability of the sigma-delta modulator, more parallel paths are required to stabilize the system. Although with this approach a world-record SNR for a 1-bit noise-shaped signal has been achieved, it is still far away from the limits imposed by information theory. As such, in practice the SNR is only limited by the amount of available computational power that is required to stabilize the higher order filters.
Erwin Janssen, Arthur van Roermund

Chapter 13. General Conclusions

Erwin Janssen, Arthur van Roermund


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