On the consistency of L2-optimal sampled signal reconstructors

Gjerrit Meinsma, Leonid Mirkin

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    Abstract

    The problem of restoring an analog signal from its sampled measurements is called the signal reconstruction problem. A reconstructor is said to be consistent if the resampling of the reconstructed signal by the acquisition system would produce exactly the same measurements. The consistency requirement is frequently used in signal processing applications as the design criterion for signal reconstruction. System-theoretic reconstruction, in which the analog reconstruction error is minimized, is a promising alternative to consistency-based approaches. The primary objective of this paper is to investigate, what are conditions under which consistency might be a byproduct of the system theoretic design that uses the L2 criterion. By analyzing the L2 reconstruction in the lifted frequency domain, we show that non-causal solutions are always consistent. When causality constraints are imposed, the situation is more complicated. We prove that optimal relaxedly causal reconstructors are consistent either if the acquisition device is a zero-order generalized sampler or if the measured signal is the ideally sampled state vector of the antialiasing ﬿lter. In other cases consistency can no longer be guaranteed as we demonstrate by a numerical example.
    Original languageUndefined
    Title of host publicationProceedings of the 19th International Symposiumon Mathematical Theory of Networks and Systems (MTNS 2010)
    EditorsE Edelmayer
    Place of PublicationBudapest
    PublisherEötvös Loránd University
    Pages1141-1145
    Number of pages5
    ISBN (Print)978-963-311-370-7
    Publication statusPublished - Jul 2010
    Event19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010 - Budapest, Hungary
    Duration: 5 Jul 20109 Jul 2010
    Conference number: 19

    Publication series

    Name
    PublisherEötvös Loránd University

    Conference

    Conference19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010
    Abbreviated titleMTNS
    CountryHungary
    CityBudapest
    Period5/07/109/07/10

    Keywords

    • IR-75720
    • EWI-18614
    • METIS-275674

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