An open electrostatic trap mass spectrometer is disclosed for operation with wide and diverging ion packets. Signal on detector is composed of signals corresponding to multiplicity of ion cycles, called multiplets. Using reproducible distribution of relative intensity within multiplets, the signal can be unscrambled for relatively sparse spectra, such as spectra past fragmentation cell of tandem mass spectrometer, past ion mobility and differential ion mobility separators. Various embodiments are provided for particular pulsed ion sources and pulsed converters such as orthogonal accelerators, ion guides, and ion traps. The method and apparatus enhance the duty cycle of pulsed converters, improve space charge tolerance of the open trap analyzer and extends the dynamic range of time-of-flight detectors.