U-Invariant Sampling: Extrapolation and Causal Interpolation from Generalized Samples (2011)
Cached
Download Links
BibTeX
@MISC{Michaeli11u-invariantsampling:,
author = {Tomer Michaeli and Volker Pohl and Yonina C. Eldar},
title = { U-Invariant Sampling: Extrapolation and Causal Interpolation from Generalized Samples},
year = {2011}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
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 problems of predicting future samples and causally interpolating deterministic signals. 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 (MRI), which correspond respectively to the translation and modulation operators. From an abstract Hilbert-space viewpoint, such sequences of functions were studied extensively in the context of stationary random processes. We thus utilize powerful tools from this discipline, although our problems are deterministic by nature. In particular, we provide necessary and sufficient conditions on the sampling mechanism such that perfect prediction is possible. For cases where perfect prediction is impossible, we derive the predictor minimizing the prediction error. We also derive a causal interpolation method that best approximates the commonly used non-causal solution. Finally, we study when causal processing of the samples of a signal can be performed in a stable manner.
Keyphrases
u-invariant sampling causal interpolation generalized sample perfect prediction unitary operator causal processing pointwise sampling sufficient condition abstract causal processing causal interpo-lation method interpolating deterministic sig-nals anti-aliasing filter audio rate conversion rich variety abstract hilbert-space viewpoint non-causal solution sampling function powerful tool stable manner modulation operator stationary random process predict-ing future sample prediction error magnetic resonance imaging on-line application signal sample
