Non-uniform signal sampling

Discrete sample representation of continuous signals without a grid



Signal sampling without a uniform grid and thus a simple Nyquist Theorem. It turns out that this generalisation is not necessarily fatal for the theory.

Reviews in a functional analysis setting are given in (Piroddi and Petrou 2004; Babu and Stoica 2010; Unser 2000; Adcock et al. 2014; Adcock and Hansen 2016).

This problem AFAICT becomes much easier if one can use priors to provide a theoretically tractable model of the nonuniformly sampled signal. The Gaussian process formalism for probabilistic spectral analysis, is one such method is even computationally tractable using the methods of e.g. Saatçi (2012).

For FFT of unevenly sampled points, you can try the Non uniform FFT. (β€œNuFFT”)

Implementations of non-uniform sampling methods.

πŸ— Lombβ€”Scargle periodogram and its uses.

References

Adcock, Ben, and Anders C. Hansen. 2016. β€œGeneralized Sampling and Infinite-Dimensional Compressed Sensing.” Foundations of Computational Mathematics 16 (5): 1263–323.
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Aldroubi, Akram, and Karlheinz GrΓΆchenig. 2001. β€œNonuniform Sampling and Reconstruction in Shift-Invariant Spaces.” SIAM Review 43 (4): 585–620.
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