RIA: Fundamentals of Delta-Sigma Modulation

施赖尔δ - σ调制构成了高度线性和可制造的模数转换器和数模转换器的基础，这些转换器被称为“过采样噪声整形”转换器。这些电路应用于窄带系统，如数字音频设备和医疗和地球物理仪器。目前，对这些非线性系统的稳定性没有足够的测试，设计者只能使用大量的计算机模拟，并希望模拟能充分地锻炼电路。本研究将解析技术与数值算法相结合，开发一种快速且完全严谨的方法来证明δ - σ调制器的鲁棒稳定性。δ - σ调制器的空载信道噪声是第二个研究课题。如何保证δ - σ调制器的非周期行为正在被展示，但仅凭这一点还不足以保证没有音调。为了判断该技术的有效性，需要使用模拟得到的数据进行听力实验。这些研究的结果正被纳入一个用于delta-sigma调制器自动设计的计算机程序中。

Schreier Delta-sigma modulation forms the foundation for the highly linear and manufacturable analog-to-digital and digital-to-analog converters known as "oversampled noise-shaping" converters. These circuits find application in narrow band systems such as digital audio equipment and medical and geophysical instrumentation. At present, there are no adequate tests for stability of these nonlinear systems - designers can only use extensive computer simulations and hope that the simulations exercise the circuit adequately. This research is developing a quick and completely rigorous method which combines analytical techniques with numerical algorithms to prove the robust stability of a delta-sigma modulator. The idle-channel noise of delta-sigma modulators is a second research topic. How to guarantee aperiodic behavior in delta-sigma modulators is being shown, but this alone is not sufficient to guarantee an absence of tones. Listening experiments using data derived from simulations need to be performed in order to judge the effectiveness of the technique. The results of these investigations are being incorporated into a computer program for the automated design of delta-sigma modulators.