Unified LMI-based design of ΔΣmodulators

Abstract

Optimal finite impulse response (FIR) error feedback filters for noise shaping in ΔΣ modulators are designed by using weighting functions based on the system norms. We minimize the weighted norms of the quantization error in the output of a ΔΣ modulator, which corresponds to the minimization of the system norm. Three norms, the H2 system norm, the (Formula presented.) system norm, and the l1 norm of the impulse response of the system, are adopted. The optimization problem for three types of FIR filters are evaluated by using linear matrix inequalities (LMIs) and then solved numerically via semi-definite programming. Design examples are provided to demonstrate the effectiveness of our proposed methods.