Recently, efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized sinc functions. This paper studies the error of the reconstructed non-bandlimited signal when an adaptive truncation scheme is employed. Further, when there are noises present in the samples, estimation on the expectation and variance of the error pertinent to the reconstructed signal is also given. Finally discussed are the reproducing properties and the Sobolev smoothness of functions in the space of non-bandlimited signals that admits such a sampling formula.