An Iterative LMI Approach to IIR Noise Transfer Function Optimization for Delta-Sigma Modulators

This paper is concerned with the issue of noise shaping of delta-sigma modulators. The shaped noise transfer function (NTF) is assumed to have infinite impulse response (IIR), and the optimization objective is minimizing the maximum magnitude of the NTF over the signal frequency band. By virtue of the generalized Kalman-Yakubovich-Popov lemma, the optimization of NTFs is converted into a minimization problem subject to quadratic matrix inequalities, and then an iterative linear matrix inequality algorithm is proposed to solve this alternative minimization problem. The proposed result overcomes the limitation of a latest method that can deal with NTFs with finite impulse response only. A design example is provided to demonstrate that the proposed design method has an advantage over the benchmark one in improving the signalto-noise ratio.