论文标题
使用任意基础函数的选择性信号外推的快速算法
A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions
论文作者
论文摘要
信号外推是将已知信号扩展到未知区域的数字信号处理中的重要任务。选择性外推是实现此目标的非常有效的算法。因此，推断是通过生成一个信号模型来获得的，该模型被用作基础函数的加权叠加。不幸的是，该算法在计算上非常昂贵，到目前为止，仅对于从离散转换发出的基础函数集而存在有效的实现。在此贡献的范围内，提出了一种新型的有效外推的有效解决方案，以使用任意基础函数利用。所提出的算法在数学上的行为与原始的选择性外推的相同，但快几十年了。此外，它能够超越存在的快速变换域算法，该算法仅限于属于相应变换的基础函数集。因此，新算法允许有效利用任意基础函数，即使它们仅是数值定义的。
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.
