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  • Research Article
  • Open Access

A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

  • 1Email author and
  • 1
EURASIP Journal on Advances in Signal Processing20112011:495394

  • Received: 7 July 2010
  • Accepted: 18 January 2011
  • Published:


Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by generating a model of the signal to be extrapolated as weighted superposition of basis functions. Unfortunately, this algorithm is computationally very expensive and, up to now, efficient implementations exist only for basis function sets that emanate from discrete transforms. Within the scope of this contribution, a novel efficient solution for Selective Extrapolation is presented for utilization with arbitrary basis functions. The proposed algorithm mathematically behaves identically to the original Selective Extrapolation but is several decades faster. Furthermore, it is able to outperform existent fast transform domain algorithms which are limited to basis function sets that belong to the corresponding transform. With that, the novel algorithm allows for an efficient use of arbitrary basis functions, even if they are only numerically defined.


  • Signal Processing
  • Basis Function
  • Digital Signal
  • Quantum Information
  • Important Task

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Authors’ Affiliations

Chair of Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, Cauerstraße 7, 91058 Erlangen, Germany


© J. Seiler and A. Kaup. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.