Robustness of aliasing-tolerant sub-Nyquist sampling with application to particle localisation

This paper proposes a novel system design for signal acquisition in Particle Tracking Velocimetry (PTV) applications. For exploiting the Finite Rate of Innovation (FRI) of these signals an appropriate sampling kernel is designed and the reconstruction process is illustrated. The main contribution is to show that aliasing effects can be neglected under certain conditions and an exact reconstruction is possible in most cases. While the sampling rate is still at least twice the FRI, it can be a fraction of the sampling kernel bandwidth. Hence, the sampling rate can be adapted to the physical process under investigation without changing the kernel designed for the worst case scenario. Considering practical aspects of the reconstruction process it is shown that even in the presence of noise precise results can be obtained.