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.
