Band-limited signal extrapolation in the presence of noise
Recently, two-step procedures for band-limited signal extrapolation have received a great deal of attention in the engineering community ([1],[2]). In this paper, we show that several two-step procedures with different underlying models can be unified by means of non-iterative algorithms for solving optimization problems in Hilbert spaces. In particular, some modifications of these procedures for noisy data are shown to be particular cases of regularization techniques for integral equations of the first kind. We present a result which gives insight into the meaning of the regularizing parameter. Some numerical examples of applying this result to signal extrapolation are shown. This unification together with those presented for iterative least-squares algorithms ([3]), and the prolate spheroidal expansion ([4]), demonstrate that most of the well-known procedures for band-limited extrapolation can be considered as special cases of standard techniques in integral equations and operator theory.