Difference Sampling Theorems For a Class of Non-Bandlimited Signals

We consider the reconstruction of a class of continuous time non bandlimited signals from its samples and their differences. The set of samples and their differences is obtained from an oversampled sequence of the underlying continuous time signal. This sequence is in turn modeled as the output of a discrete time multirate interpolation filter. Using this model, we propose a general structure to retrieve the continuous time signal and derive corresponding mathematical conditions for its reconstruction using FIR digital filters. The use of FIR filtering is desired to guarantee the stability of the reconstruction process