One-bit Sigma-Delta modulation on the circle

Manifold models in data analysis and signal processing have become more prominent in recent years. In this paper, we will look at one of the main tasks of modern signal processing, namely, at analog-to-digital (A/D) conversion in connection with a simple manifold model - the circle. We will focus on Sigma-Delta modulation which is a popular method for A/D conversion of bandlimited signals that employs coarse quantization coupled with oversampling. Classical Sigma-Delta schemes provide mismatches and large errors at the initialization point if the signal to be converted is defined on the circle. In this paper, our goal is to get around these problems for Sigma-Delta schemes. Our results show how to design an update for the first and the second order schemes based on the reconstruction error analysis such that for the updated scheme the reconstruction error is improved.

Automated summary

Manifold models are increasingly important in data analysis and signal processing. This paper focuses on one specific task in modern signal processing, which is the analog-to-digital (A/D) conversion using Sigma-Delta modulation. The paper addresses the issue of mismatches and large errors in classical Sigma-Delta schemes when the signal is defined on a circle. The authors propose an updated scheme based on reconstruction error analysis that improves the accuracy of the reconstruction.