Sampling from a system-theoretic viewpoint

Gjerrit Meinsma, Leonid Mirkin

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    This paper studies a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is ��?xed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the $L^2$-norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is $l$-causal for a given $l\geq 0,$ i.e., that its impulse response is zero in the time interval $(-\infty,-l h),$ where $h$ is the sampling period. We derive a closed-form state-space solution of the problem, which is based on the spectral factorization of a rational transfer function.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages46
    Publication statusPublished - Nov 2009

    Publication series

    PublisherDepartment of Applied Mathematics, University of Twente
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850


    • MSC-94A20
    • MSC-93E24
    • EWI-16463
    • MSC-94A12
    • IR-68292
    • Wiener ��?ltering
    • MSC-49N05
    • MSC-49N10
    • MSC-93B28
    • MSC-93B36
    • MSC-93B50
    • MSC-93C57
    • MSC-93B51
    • Cardinal splines
    • METIS-264127
    • MSC-93D25
    • Lifting
    • Down sampling
    • Shannon formula
    • MSC-93E14
    • MSC-93E11
    • Hybrid model matching
    • Sampling
    • Wiener filtering

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