This paper deals with the problem of reconstructing a band-limited signal when a nite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for band-limited functions and the relative oversampling formulas. We study the eigenvalues of the matrices arising in the procedure of recovering the lost samples, nding estimates of their eigenvalues and their dependence on the oversampling parameter and on the number of missing samples. When the missing samples are consecutive, the problem may become very ill-conditioned. We present a numerical procedure to overcome this diculty, also in presence of noisy data, by using the Tikhonov regularization technique.
Stability of the Recovery of Missing Samples inDerivative Oversampling
BRIANZI, PAOLA;DEL PRETE, VINCENZA
2011-01-01
Abstract
This paper deals with the problem of reconstructing a band-limited signal when a nite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for band-limited functions and the relative oversampling formulas. We study the eigenvalues of the matrices arising in the procedure of recovering the lost samples, nding estimates of their eigenvalues and their dependence on the oversampling parameter and on the number of missing samples. When the missing samples are consecutive, the problem may become very ill-conditioned. We present a numerical procedure to overcome this diculty, also in presence of noisy data, by using the Tikhonov regularization technique.
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