Matched sampling systems, relation to wavelets and implementation using PRCC filter banks

This paper deals with two types of sampling systems; namely, the interpolat ion and approximation sampling systems. Closed-form expressions are derived for the frequency responses of the filters used in these systems that are matched to the input process in the mean squared sense, Closed-form express ions are also derived for the mean squared error between the input and the reconstructed processes for these matched sampling systems. Using these exp ressions, it is shown that the Meyer scaling function and wavelet or functi ons derived from these arise naturally in the con text of subsampled bandli mited processes. To implement these systems, the perfect reconstruction cir cular convolution (PRCC) filter bank is proposed as a framework for the fre quency-sampled implementation of these systems. Examples of matched interpo lation and approximation sampling systems are provided, and their performan ce is compared with some standard interpolators to demonstrate their effica cy.