A method for mass analyzing ions in an ion trap, comprising: (a) confining ions of different mass-to-charge ratios (m/z's) in a trap volume by applying a trapping signal to the ion trap; (b) mass sequentially ejecting the confined ions to a detector by applying a resonant excitation signal to the ion trap and progressively scanning the trapping signal amplitude over time, wherein at least one of: (i) a scan starting time, (ii) a frequency of the resonant excitation signal or the trapping signal, or (iii) a phase of the resonant excitation signal or the trapping signal, is or are controlled to cause ions of a particular m/z to be ejected in a reproducible pattern of plural micropulses, wherein the frequencies of the trapping and resonant excitation signals are fractions of each other, further wherein the patterns of plural micropulses are repeating based on the phase relationships between the trapping signal and the resonant excitation signal; the method characterized by: (c) generating at the detector a plurality of measurement points extending over a time range, each measurement point representing an intensity of ejected ions detected at a discrete timepoint, at a data acquisition frequency sufficiently high to resolve adjacent micropulses; (d) determining a linear combination of stored micropulse patterns that approximates the plurality of measurement points, wherein each stored micropulse pattern corresponds to an ion of a particular m/z and wherein the stored micropulse patterns define a repeating sequence over an m/z interval; and (e) constructing a mass spectrum based on the determined linear combination of stored micropulse patterns. (a) confining ions of different mass-to-charge ratios (m/z's) in a trap volume by applying a trapping signal to the ion trap; (b) mass sequentially ejecting the confined ions to a detector by applying a resonant excitation signal to the ion trap and progressively scanning the trapping signal amplitude over time, wherein at least one of: (i) a scan starting time, (ii) a frequency of the resonant excitation signal or the trapping signal, or (iii) a phase of the resonant excitation signal or the trapping signal, is or are controlled to cause ions of a particular m/z to be ejected in a reproducible pattern of plural micropulses, wherein the frequencies of the trapping and resonant excitation signals are fractions of each other, further wherein the patterns of plural micropulses are repeating based on the phase relationships between the trapping signal and the resonant excitation signal; (c) generating at the detector a plurality of measurement points extending over a time range, each measurement point representing an intensity of ejected ions detected at a discrete timepoint, at a data acquisition frequency sufficiently high to resolve adjacent micropulses; (d) determining a linear combination of stored micropulse patterns that approximates the plurality of measurement points, wherein each stored micropulse pattern corresponds to an ion of a particular m/z and wherein the stored micropulse patterns define a repeating sequence over an m/z interval; and (e) constructing a mass spectrum based on the determined linear combination of stored micropulse patterns.