Signal Processing for Digital Analog Interface

摘要：这项研究探索了如何利用编码和信号处理技术来构建更好的模数和数模转换器，创建更好的数字印刷半色调算法，以及改进医学成像。所有这些以及许多其他应用都使用一种称为Sigma Delta调制的技术。Sigma Delta调制是一种允许从二进制量化数据生成高精度信号的技术。这项研究通过将Sigma DelTamodation视为优化问题的贪婪解而不是具有反馈的线性系统，从而提供了对Sigma DelTammodation的新的解释。这种新的观点不仅解释了现有的Sigma Delta调制器的工作原理，而且还建议了一种全新的调制器结构连续体，它可以在复杂性和性能之间进行权衡。这项研究有两个主要目的，一个是实用的和实验的，另一个是理论的，实际的目的是改进现有的传统Sigma Delta调制器设计的经验方法，并使其适应优化方法提出的新的调制器结构。这项研究应该会对目前使用Sigma Delta调制器的众多领域以及由于这项研究而变得可行的新应用产生立竿见影的好处。理论主旨将发展对量子化过程的严格理解。

Abstract:This research explores how techniques from coding and signal processing can beused to build better analog to digital and digital to analog converters, create better half toning algorithmsfor digital printing,and improve medical imaging. All of these as well as many other applications use a technique calledSigma Delta modulation. Sigma Delta modulation is a technique which allows high precisionsignal to be generated from binary quantized data. This research provides a new interpretation of Sigma Deltamodulation by viewing it as a greedy solution to an optimization problem insteadof a linear system with feedback.This new view not only explains how existing Sigma Delta modulators work but alsosuggests a whole new continuum of modulator structures which cantrade complexity against performance. The research has two mainthrusts, one practical and experimental and the other theoretical.The practical thrust will improve upon the existing empiricalapproaches to conventional Sigma Delta modulator design and thenadapt them to new modulator structures suggested by the optimizationapproach. This research should yield immediate benefits for thenumerous areas where Sigma Delta modulators are used now as wellas new applications that will become viable because of thisresearch. The theoretical thrust will develop a rigorousunderstanding of the quantization process.