Recently, an increased emphasis has been placed on the ability to make mass measurements with high accuracy and precision. The motivation for this is that high-precision mass measurements, together with isotope intensity matching, permit confirmation of molecular formulas and de novo molecular formula prediction, both of which enhance the value of proteomics and metabolomics data. The confidence of mass-based conclusions also depends on reliable estimates of uncertainty. However, determining the precision of a particular measurement remains a complicated process. For signals which are well-resolved and of sufficient intensity, an often-overlooked factor for high precision is the mass sampling frequency (abscissa, Delta x). We have analyzed the impact of Delta x on the centroid calculation of peak position, and find that existing quality standards, such as 4 or 5 samples per peak, may not be sufficient to achieve high precision. Time-domain and m/z-domain sampling frequency on time-of-flight (TOF) mass analyzers can be improved using a new method that we call Physical Signal Modulation (PSM). PSM allows very substantial improvements by decreasing Delta x without requiring specialized hardware or digitizers. In addition to providing accuracy improvements, PSM also dramatically improves signal-to-noise ratios by removing coherent noise. Software to perform PSM data processing is available as part of the PySpecTools package. Copyright (C) 2011 John Wiley & Sons, Ltd.