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Convergence analysis of an iterative method for the reconstruction of multi-band signals from their uniform and periodic nonuniform samples
, Article Sampling Theory in Signal and Image Processing ; Volume 7, Issue 2 , 1 May , 2008 , Pages 113-129 ; 15306429 (ISSN) ; Marvasti, F ; Sharif University of Technology
2008
Abstract
One of the proposed methods for recovery of a band-limited signal from its samples, whether uniform or nonuniform, is the so-called Frame Method. In this method the original signal is reconstructed by iterative use of sampling-filtering blocks. Convergence of this method for linear invertible operators has been previously proved. In this paper we show that this method for non-invertible periodic nonuniform samplings as well as non-invertible uniform samples of bandpass (or multi-band) signals will lead to the pseudo-inverse solution. Convergence conditions in case of additive noise will also be discussed. © 2008 Sampling Publishing