Continuous-time reconstruction of nonuniform sampled signals on a band-limited wavelet basis

We propose a reconstruction method of continuous-time random signals by fitting nonuniform samples to a band-limited continuous-time wavelet basis. Based on wavelet analysis, our method uses a windowing technique with variable-sized intervals, taking advantage of the nonuniform signal sampling. This method leads to analytical formulas for the reconstructed continuous-time signal, and as well as for its derivatives. This can be very useful to perform a parametric estimation of so-called continuous-time ARMA models adopted for continuous-time random signals modeling. Several parameters like mother wavelet type, time shift interval between consecutive wavelets and resolution levels number can be adapted. In this paper, we describe the principle of the proposed reconstruction method and discuss its performance