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Generalised sampling theory with rational sampling factors

The authors consider the problem of reconstructing a signal from the outputs of several systems, which are sampled with periods related by rational factors. They present a unified framework in terms of which generalised sampling theories presented by previous researchers can be discussed. Using the spectral aliasing matrix (SAM), the modelling of generalised sampling can be studied in the cases of both bandlimited and non-bandlimited input signals. In comparison with the generalised sampling theories by Papoulis, Brown and some other scientists, which were based on the same sampling rate, they extend the theory by introducing the SAM and formulating sampling in an elegant matrix representation and considering generalised sampling of different sampling rates with rational factors. Several solution methods of the derived system of linear equations are presented. These methods can also be applied in both the band-limited and the non-band-limited input signal cases, and the easiest reconstruction implementation can be chosen in the temporal or the frequency domain. Finally, they present some experimental results with a one-dimensional signal designed to test the performance of the proposed algorithm for various sampling rates and under different noise conditions.