Weighted median filters with sigma-delta modulation encoding

Digital decimation filters play a fundamental role in oversampled sigma–delta A/D decoders. In this paper, we first show that weighted median (WM) filtering of a demodulated sequence (at the Nyquist rate) can be implemented concurrently in the A/D decoder. Through a simple modification of the binary time-series outputted by the A/D modulator, the sequence obtained after the SDM decoder is shown to be equivalent to WM filtering the multilevel sequence at the Nyquist rate. Second, we show that WM filters can be used for SDM decimation filters and that these filters are readily implemented in the SDM binary domain. A very promising characteristic of SDM converters equipped with WM decimating filters is that sharp discontinuities (edges) can be preserved and acquired. Thus, the bandlimited constraint imposed on the input signals can be relaxed making SDM more attractive to A/D conversion of signals containing sharp transitions. The proposed signal processing algorithms, in essence, combine A/D sigma–delta converters and WM filters into a single programmable system.