Weighted median filters with sigma-delta modulation encoding

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