A method of processing Fourier Transform Mass Spectrometry (FTMS) data comprises carrying out a Fourier Transform of a part of a time domain transient and identifying from that transformed data signal peaks representative of the presence of ions. Once the peaks have been identified, the full transient is then transformed, and the peaks identified in the partial transient transform are used to locate true peaks in the transformed full transient. The number of 'false' peaks resulting from random noise has been found to correlate to the resolution, so that using a partial transient to identify true peaks reduces the risk of false peaks being included; nevertheless this information can then be applied to the full data set when transformed. As an alternative, different parts of the full data set can be transformed and then correlated; because any noise will be random, false peaks should occur at different places in the two partial transforms.