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

This paper deals with two types of sampling systems, namely, the interpolation 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 expressions are also derived for the mean squared error between the input and the reconstructed processes for these matched sampling systems. Using these expressions, it is shown that the Meyer scaling function and wavelet or functions derived from these arise naturally in the context of subsampled bandlimited processes. To implement these systems, the perfect reconstruction circular convolution (PRCC) filter bank is proposed as a framework for the frequency-sampled implementation of these systems. Examples of matched interpolation and approximation sampling systems are provided, and their performance is compared with some standard interpolators to demonstrate their efficacy