Multi-channel sampling with periodic non-uniform samples

Abstract

Taking a filtered signal is a general method in sampling theory. Reconstucting the original signal from the signals, which passed through several filters, is Multi-channel sampling. Through this Multi-channel sampling, we can expand sampling period in proportion to the number of filters. Thus, we can recover the function by sampling from various types of samples. In this paper, we will get out of existing regular sampling and recover the signal by using samples $\{L_jf(a_m+r(Mn+m))\}_{n\in\mathbb{Z}, j=1,...,s, m=0,..., M-1}$. and through the theoretical approach to periodic non-uniform sampling, we analyze the relationship between this method and generalized regular sampling.