Naslov
Sampling of Signals in Shift-Invariant Spaces and Sparse Signal Reconstruction

Autori
Vlašić, Tin

Izvornik
Online/Web

Vrsta, podvrsta
Ostale vrste radova, ostali radovi sa studija

Godina
2019

Ključne riječi
signal sampling, signal reconstruction, Shannon’s sampling theorem, beyond Nyquist, shift-invariant subspace, B-splines, signal innovation, finite rate of innovation (FRI), compressive sampling, optimization problem, sparse modeling

Sažetak
This paper is a survey of the current state of signal sampling and reconstruction. The focus is on regular sampling, where the grid is uniform. We reinterpret classical sampling procedure as an orthogonal projection onto the subspace of bandlimited functions. The reinterpretation is used to extend the classical sampling theorem for a representation of signals in a more general class of shift-invariant subspaces. This allows simpler and more realistic interpolation models, and a much wider class of prefilters that are not ideal low-pass anymore. We continue with a topic that received growing attention recently and that is sampling and reconstruction of signals that are known to be sparse in some domain. We present two major paradigms: sampling of signals with finite rate of innovation and compressed sensing, both of which can reconstruct the signal from far less samples than the standard sampling method. While the finite rate of innovation work recovers signals that have a sparse parametric notation in the time-domain, such as non-uniform splines and piece- wise polynomials, compressed sensing typically recovers signals that are sparse in some transform domain. We present the idea of the annihilating filter and the recovery of a periodic stream of Diracs using the finite rate of innovation reconstruction method. In the compressed sensing part, the interest is on sampling and reconstruction of analog continuous-time signals and the techniques of extending the compressed sensing paradigm to the analog domain.

Izvorni jezik
Engleski

Znanstvena područja
Elektrotehnika

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