Sampling systems matched to input processes and their implementation using PRCC filter banks

This paper introduces a novel filter bank structure called the perfect reconstruction circular convolution (PRCC) filter bank. These filters satisfy the perfect reconstruction properties, namely, the paraunitary conditions, in the discrete frequency domain. The development of the PRCC framework has been motivated by the need for an efficient, invertible algorithm for the implementation of the discrete wavelet transform (DWT) based on bandlimited scaling functions and wavelets. As a motivation, we show how bandlimited scaling functions arise naturally in the context of interpolation and approximation sampling systems with the filters matched to the input process. Next, we show how the PRCC filter bank framework serves as a basis for a frequency sampled implementation of DWT based on bandlimited scaling functions and wavelets, and in general, of matched filters in the above sampling systems. Finally, we present simulation results using the PRCC framework which verify that the matched interpolating function gives the smallest mean squared error between the input and the reconstructed signal, as compared to other interpolating functions.