Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming

TL;DR

This paper proposes a novel optimization framework for designing the noise transfer function of Delta-Sigma modulators, focusing on output filter properties rather than input features, using semi-definite programming and the KYP lemma.

Contribution

It introduces a new method for optimizing NTF design based on output filter characteristics, improving performance over traditional input-based approaches.

Findings

The proposed method outperforms standard NTF design strategies in practical scenarios.

Semi-definite programming effectively shapes NTFs according to output filter requirements.

The framework is applicable to D/D and D/A conversion and actuation systems.

Abstract

The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically designed after the features of the input signal. We suggest that in many applications, and notably those involving D/D and D/A conversion or actuation, the NTF should instead be shaped after the properties of the output/reconstruction filter. To this aim, we propose a framework for optimal design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite programming. Some examples illustrate how in practical cases the proposed strategy can outperform more standard approaches.