Optimal filtering of incremental first-order sigma-delta modulators with sweep input

In this paper, an optimal filter design procedure is described, from the equation representing the behaviour of a ΣΔ modulator to a functional algorithm. The first section shows the design of an optimal filter for a first-order ΣΔ ADC with a constant input. Next, an algorithm for a time-varying input is detailed. The last algorithm allows an optimal decoding of high-resolution ADCs without an SH circuit.