Weighted median filters with sigma-delta modulation encoding

Oversampled Sigma-Delta modulation (SDM) is becoming a standard method for implementing high-resolution A/D and D/A converters in silicon. Digital decimation lters play a fundamental role in Oversampled Sigma-Delta A/D decoders. In this paper, we rst show that Weighted Median Filters (WMF) can be used for SDM decimation lters and that these lters are readily implemented in the SDM binary domain. A very promising characteristic SDM converters equipped with weighted median decimating lters is that sharp discontinuities (edges) can be preserved and acquired. Thus, the bandlimited constraint imposed on the input signals could be relaxed making SDM more attractive to A/D conversion of signals containing sharp transitions. Secondly , we show that weighted median ltering of a demodulated sequence (at the Nyquist rate) can be implemented concurrently in the A/D decoder. Thus, by a simple modiication of the binary time-series outputted by the A/D modulator, the sequence obtained after the SDM demodulator is shown to be equivalent to weighted median ltering the multilevel sequence at the Nyquist rate. The proposed signal processing algorithms, in essence, combine A/D sigma-delta converters and weighted median lters into a single programmable system. A joint WMF and SDM A/D tunnable converter, can be used in speech and audio applications in (possibly) noisy environments.