Filtering, Sampling, and Reconstruction With Time-Varying Bandwidths

The effective bandwidth of a signal can significantly vary in time. To improve sampling efficiency, it would be desirable, therefore, to be able to sample at a correspondingly time-varying rate while maintaining the ability to stably reconstruct the signal from its samples. Fourier theory is too rigid for this purpose but functional analytic tools have allowed a suitable generalization of Shannon sampling. Here, we add to this generalized sampling theory by constructing the corresponding time-varying prefilter. The new filtering technique should open the generalized sampling method to a wide range of applications.