Robust Filter Design for Uncertain 2-1 Sigma-Delta Modulators via the Central Polynomial Method

Uncertainty in the integrators of 2-1 sigma-delta modulators causes imperfect cancellation of first stage quantization noise, and reduces signal-to-noise ratio in analogue-to-digital converters. Design of robust matching filters based on convex optimization over uncertain linearized state-space representations gives complicated models and high-order designs. This letter describes a polynomial design method leading to simpler multilinear models and fixed-order filters. The modulators are cast as a polynomial polytope, and filters satisfying an Hinfin bound arise from solving linear matrix inequalities (LMIs). Results at low frequency show the proposed filter outperforming the nominal one, with a performance close to the estimated optimum.