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    On exact and optimal recovering of missing values for sequences

    247729.pdf (608.3Kb)
    Access Status
    Open access
    Authors
    Dokuchaev, Nikolai
    Date
    2017
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Dokuchaev, N. 2017. On exact and optimal recovering of missing values for sequences. Signal Processing. 135: pp. 81-86.
    Source Title
    Signal Processing
    DOI
    10.1016/j.sigpro.2016.12.024
    ISSN
    0165-1684
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/19145
    Collection
    • Curtin Research Publications
    Abstract

    The paper studies recoverability of missing values for sequences in a pathwise setting without probabilistic assumptions. This setting is oriented on a situation where the underlying sequence is considered as a sole sequence rather than a member of an ensemble with known statistical properties. Sufficient conditions of recoverability are obtained; it is shown that sequences are recoverable if there is a certain degree of degeneracy of the Z-transforms. We found that, in some cases, this degree can be measured as the number of the derivatives of Z-transform vanishing at a point. For processes with non-degenerate Z-transform, an optimal recovering based on the projection on a set of recoverable sequences is suggested. Some robustness of the solution with respect to noise contamination and truncation is established.

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