A method, comprising: receiving a plurality of 2-tuples of asynchronously sampled inputs at an asynchronous to synchronous reconstructor; performing a coarse asynchronous to synchronous conversion using the plurality of 2-tuples to generate a plurality of low precision synchronous outputs; generating a high precision synchronous output, z0, using a plurality of asynchronous 2-tuples, low precision synchronous outputs after it, and its own high precision outputs from previous steps; calculating c0 and c−1 by summing future low precision outputs and the past high precision outputs after they are weighted with the appropriate windowed sinc. values and then subtracted from appropriate asynchronous samples; calculating, the four quantities “s−11”, “s01”, “s00” and “s−10” based on particular values of the windowed sinc. function; and using c0, c−1, s−11, s01, s00 and s−10, the high precision synchronous output of interest, z0 is generated.