Designing fast interpolation and extrapolation algorithms

One of the purposes of this paper is to outline a unified approach to the design of fast, stable band-limited interpolation or extrapolation l superresolution algorithms, iterative or noniterative, able to perform well even for large size problems (block sizes of thousands of samples and above). The results are about one-dimensional signals, but some attention is given to efficient image extrapolation or superresolution. An attempt is also made to clarify the connections between some of the existing algorithms, and in the process of doing so we uncover some new possibilities, that lead to the fastest known algorithms for certain classes of problems. However, it is shown that no method can be “best overall”, since there are problems for which one set of methods clearly outperforms the others. The main issues that arise when designing efficient algorithms for the solution of a specific problem are discussed