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

TY - JOUR

T1 - Robust Filter Design for Uncertain 2-1 Sigma-Delta Modulators via the Central Polynomial Method

AU - McKernan, John

AU - Gani, Mahbub

AU - Henrion, Didier

AU - Yang, Fuwen

PY - 2008

Y1 - 2008

N2 - 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 H-infinity 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.

AB - 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 H-infinity 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.

U2 - 10.1109/LSP.2008.2003992

DO - 10.1109/LSP.2008.2003992

M3 - Article

SN - 1558-2361

VL - 15

SP - 737

EP - 740

JO - IEEE SIGNAL PROCESSING LETTERS

JF - IEEE SIGNAL PROCESSING LETTERS

ER -