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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...
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...
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...
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...
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,...
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...
In chapter eight, an efficient derivative of the Trellis sigma-delta modulator, called the Efficient Trellis sigma-delta modulator, is introduced. Instead of exploring 2N solutions in parallel, only M solutions out of the possible 2N are tracked. This is possible since only a fraction of all the 2N solutions contributes to...
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...
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...
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...
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...
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