Sampling from a system-theoretic viewpoint: Part II - Noncausal solutions

Gjerrit Meinsma, Leonid Mirkin

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    Abstract

    This paper puts to use concepts and tools introduced in Part I to address a wide spectrum of noncausal sampling and reconstruction problems. Particularly, we follow the system-theoretic paradigm by using systems as signal generators to account for available information and system norms (L2 and L∞) as performance measures. The proposed optimization-based approach recovers many known solutions, derived hitherto by different methods, as special cases under different assumptions about acquisition or reconstructing devices (e.g., polynomial and exponential cardinal splines for fixed samplers and the Sampling Theorem and its modifications in the case when both sampler and interpolator are design parameters). We also derive new results, such as versions of the Sampling Theorem for downsampling and reconstruction from noisy measurements, the continuous-time invariance of a wide class of optimal sampling-and-reconstruction circuits, etcetera.
    Original languageUndefined
    Pages (from-to)3591-3606
    Number of pages16
    JournalIEEE transactions on signal processing
    Volume58
    Issue number7
    DOIs
    Publication statusPublished - Jul 2010

    Keywords

    • Least-square optimization
    • Lifting
    • Wiener filtering
    • Sampling and reconstruction
    • Shannon formula
    • Min-max optimization
    • EWI-18611
    • METIS-277435
    • IR-73705
    • Cardinal splines
    • Non-causal filters

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