Recursive Laguerre and Kalman filters as efficient full-rate sigma–delta (Σ-ΔΣ-Δ) demodulators

Over the last few decades, the use of sigma–delta (Σ–Δ) modulators, has moved into various signal processing and communication application areas. Usually, Σ–Δ modulators produce single-bit outputs and thus are well suited for VLSI circuits that could be implemented using a small number of multipliers. For improved signal-to-noise (quantization) performances, higher-order modulator schemes with multi-loop and multi-stage architecture are utilized in most of the Σ–Δ applications. The quantization noise behavior of these higher-order modulators is well understood. Based on the quantization noise characteristics, various demodulator filter architectures, such as optimal FIR, Sinc filter and non-linear filters are reported in the literature. In this paper, we propose efficient recursive filters that could be used as the demodulator filter. In particular, a Laguerre filter architecture and a Kalman filter architecture are described. In usual Σ–Δ architecture, the demodulator filter operates at a lower (down-sampled) rate. However, in certain applications a full-rate (FR) demodulator is needed to achieve a high signal-to-noise ratio. It will be demonstrated that the proposed recursive filters are ideally suitable for FR demodulator applications.