Optimal FIR Filter Design based on Curve Fitting Approximation for Uncertain 2–1 Sigma–Delta Modulator

Uncertain components in the integrators of 2–1 Sigma–Delta modulators cannot eliminate the first stage quantization noise completely, and the signal-to-noise ratio in analogue-to-digital converters is not reduced perfectly either. In order to solve the matching problem, older filter designs based on convex optimization are mathematically complicated, computationally intensive and not so efficient in application. In this paper, we propose a design method based on curve fitting approximation for uncertain linearized model of the modulator which is simple in principle and practical in application. Simulation results show that the optimal filter has better performance on multiple validations when compared to other modulator filters.