Non-uniform signal sampling

Discrete sample representation of continuous signals without a grid

January 8, 2019 — August 7, 2023

dynamical systems
Hilbert space
signal processing
statistics
time series

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Figure 1

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.

There are reviews in a functional analysis setting (; ; ; ; ).

This problem, as far as I can tell, becomes much easier to state if one can use priors to provide a theoretically tractable model of the non-uniformly sampled signal. The Gaussian process formalism for probabilistic spectral analysis is one such method and is even computationally tractable using the methods of e.g. Saatçi ().

For FFT of unevenly sampled points, you can try the Non-uniform FFT (“NuFFT”).

Implementations of non-uniform sampling methods:

🏗 Lomb—Scargle periodogram and its uses.

1 Neural methods

For now, see implicit neural representations and neural ODEs.

2 References

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