On incremental sigma-delta modulation with optimal filtering

The paper presents a quantization-theoretic framework for studying incremental sigma-delta (ΣΔ) data conversion systems. The framework makes it possible to efficiently compute the quantization intervals and hence the transfer function of the quantizer, and to determine the mean square error (MSE) and maximum error for the optimal and conventional linear filters for first and second order incremental ΣΔ modulators. The results show that the optimal filter can significantly outperform conventional linear filters in terms of both MSE and maximum error. The performance of conventional ΣΔ data converters is then compared to that of incremental ΣΔ with optimal filtering for bandlimited signals. It is shown that incremental ΣΔ can outperform the conventional approach in terms of signal-to-noise-and-distortion ratio. The framework is also used to provide a simpler and more intuitive derivation of the Zoomer algorithm.