Reproducible Research: A Case Study of Sampling Signals with Finite Rate of Innovation

Abstract

A case study on reproducible research in sampling theory of signals containing a finite rate of innovation is the topic of this paper. By building a solid research which is furthermore reproducible enables the researcher to build intuition in a research area and to progress at a much faster pace. Here, we show that the founding problem of sampling and exact reconstruction of periodic streams of Dirac pulse will be the basis of the sampling theory for signals with finite rate of innovation. The sampling theory can be extended to other signals such as piecewise polynomials, bandlimited signals with additive shot noise and the sum of bandlimited signals with piecewise polynomial signals. It is shown that the implementation is based on the one for streams of Dirac pulses, thus making the new research reproducible as well.