B-spline based perfect reconstruction of non band limited noisy signals

Abstract

We consider the problem of sampling non band limited signals with a finite number of degrees of freedom, i.e. non uniform splines or piecewise polynomials. These signals are typically called signals with finite rate of innovation (FRI). We propose a novel technique for perfectly reconstructing impulses of Diracs. These Diracs are our adopted non band limited signal and have been filtered specifically through a B-spline sampling kernel, and then been uniformly sampled with a period T: This B-spline sampling kernel has an impulse response that is similar to most linear acquisition sensors/devices. The novelty of our proposed approach lies in the fact that it is robust in noisy environments, unlike many recent similar techniques, i.e. Dragotti et al. [1], that may provide faster implementation but are very delicate with any type of noise. Our technique also does not have any restrictions on the number of perfectly reconstructed Diracs with respect to the sampling kernel order and achieves its reconstruction in a B-spline 2-channel perfect reconstruction (PR) framework. A comparison of our proposed B-spline based perfect reconstruction system with the recent technique given in [1], in terms of speed, amount of noise and kernel order, is provided.