Two novel block-based algorithms are presented for the reconstruction of uniform samples given the nonuniform samples. The first algorithm uses a sinc interpolator whereas the second one uses a DFT-based interpolator. It is shown that the proposed algorithms are stable and the error due to noise and sampling jitter is bounded by the corresponding error norms of noise and jitter, respectively. We show that both of the block-based algorithms provide nearly perfect reconstruction for a class of practically time and bandlimited signals. Boundary effects are considered and single and multiblock processing is discussed. A modified block-based algorithm is developed by using the windowing technique in order to improve the mean-squared error (MSE) performance for nonbandlimited signals. It is shown that this algorithm performs better than a group of alternative algorithms, including Yen's third algorithm, for a variety of signal, noise, and sampling grids.