After calculating the bin number for each peak at each possible charge state, we added the intensity into a 50×N matrix (Figure and), where N is the total number of bins. Each row represents a different charge state from 1-50, used in the calculations above. Thus, the phase must be calculated for each m/z data point and each possible charge state, but the relatively simple math operations make this process fast. After summing all points into the matrix, there are strong intensities in the matrix for rows where the charge state is equal to the correct charge state or a higher harmonic. Note, it is not possible to reverse the operation of phase encoding. Information on both the absolute m/z and each peak intensity is lost in the process. Thus, this encoding is likely not useful for other applications like segmenting which peaks belong to a cluster. However, we found that this phase/mass defect encoding was both fast and informative for charge state assignments, yielding superior accuracy to other encoding approaches tested.