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Optimal random sampling for spectrum estimation in DASP applications

Andrzej Tarczynski, Dongdong Qu (2005)

International Journal of Applied Mathematics and Computer Science

In this paper we analyse a class of DASP (Digital Alias-free Signal Processing) methods for spectrum estimation of sampled signals. These methods consist in sampling the processed signals at randomly selected time instants. We construct estimators of Fourier transforms of the analysed signals. The estimators are unbiased inside arbitrarily wide frequency ranges, regardless of how sparsely the signal samples are collected. In order to facilitate quality assessment of the estimators, we calculate...

Recovery of band-limited functions on locally compact Abelian groups from irregular samples

H. G. Feichtinger, S. S. Pandey (2003)

Czechoslovak Mathematical Journal

Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group G . The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative...

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

Dryanov, Dimiter (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.We characterize Paley-Wiener-Schwartz space of entire functions as a union of three-parametric linear normed subspaces determined by the type of the entire functions, their polynomial asymptotic on the real line, and the index p ≥ 1 of a Sobolev type Lp-summability on the real line with an appropriate weight function. An entire function belonging to a sub-space of the decomposition is exactly recovered by a sampling series, locally...

Variantes sur un théorème de Candès, Romberg et Tao

Jean-Pierre Kahane (2013)

Annales de l’institut Fourier

Le théorème CRT dit comment reconstruire un signal à partir d’un échantillonnage de fréquences parcimonieux. L’hypothèse sur le signal, considéré comme porté par un groupe cyclique d’ordre N , est qu’il est porté par un petit nombre de points, s , et la méthode est de choisir aléatoirement C s log N fréquences et de minimiser dans l’algèbre de Wiener le prolongement à ℤ / N ℤ de la transformée de Fourier du signal réduite à ces fréquences. Quand C est grand, la probabilité de reconstruire le signal est voisine...

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