Causal signal recovery from U-invariant samples

Causal processing of a signal´s samples is crucial in on-line applications such as audio rate conversion, compression, tracking and more. This paper addresses the problem of causally reconstructing continuous-time signals from their samples. We treat a rich variety of sampling mechanisms encountered in practice, namely in which each sampling function is obtained by applying a unitary operator on its predecessor. Examples include pointwise sampling at the output of an anti-aliasing filter and magnetic resonance imaging, which correspond respectively to the translation and modulation operators. Such sequences of functions were studied extensively in the context of stationary random processes. We thus utilize powerful tools from this discipline, to derive a causal interpolation method that best approximates the commonly used non-causal reconstruction formula.