  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.
