A new formula for lost sample restoration

The reconstruction of oversampled band-limited random signals from incomplete discrete data is addressed. The proposed reconstruction scheme stems from Lagrange interpolation formula such as the Shannon cardinal expansion. However, the proposed formula explicitly takes into account the possible loss of one or more samples. The formula can be fitted to any sample loss or deterioration by a simple time index translation. The reconstruction performance is studied with respect to the number of lost samples, to the number of available samples and to the oversample rate. The proposed scheme, associated to specific interpolation functions, results in a high convergence rate even in the neighborhood of the lost samples providing an accurate sample restoration method.

1. Introduction

Let denote a zero mean stationary process, with regular band-limited spectrum in defined by: $$\begin{equation*} E[Z(t)Z^{\ast}(t-\tau)]=\int_{-\pi}^{\pi}e^{i\omega\tau}s(\omega)d\omega \tag{1}\end{equation*}$$