Reconstruction method for reconstructing a first signal (x(t)) regularly sampled at a sub-Nyquist rate, comprising the step of retrieving from the regularly spaced sampled values (ys[n], y(nT)) a set of weights (cn, cnr, ck) and shifts (tn, tk) with which said first signal (x(t) can be reconstructed. The reconstructed signal (x(t) can be represented as a sequence of known functions ( gamma (t) weighted by the weights (ck) and shifted by the shifts (tk). The sampling rate is at least equal to the rate of innovation ( rho ) of the first signal (x(t)).