A robust control approach to perfect reconstruction of digital signals

Abstract

In this paper we present a deterministic worst-case approach for reconstructing discrete-valued signals that have been filtered via dispersive and noisy systems ("channels"). This approach, which is explored based on robust control ideas and makes no assumption on the noise (distribution or structure) other than a requirement that its magnitude be bounded, can serve as a complement to existing approaches that attempt to reconstruct discrete-valued signals by optimizing probabilistic criteria. The particular problems touched upon are: (i) necessary and sufficient conditions for causal (possibly delayed) perfect reconstruction under deterministic magnitude bounded noise for single-input single-output (SISO) and multi-input multi-output (MIMO) channels; (ii) perfect reconstruction based on decision feedback (DF) structures; and (iii) necessary and sufficient conditions for perfect reconstruction with DF structures in the presence of uncertainties in the channel. The ℓ1 control theory emerges as the natural key player for analysis and synthesis of perfect reconstructing strategies in this framework. © 2007 IEEE.