Open Access

A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

  • Jürgen Seiler (EURASIP Member)1Email author and
  • André Kaup (EURASIP Member)1
EURASIP Journal on Advances in Signal Processing20112011:495394

Received: 7 July 2010

Accepted: 18 January 2011

Published: 27 January 2011


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 ProcessingBasis FunctionDigital SignalQuantum InformationImportant Task

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Authors’ Affiliations

Chair of Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, 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.