A gaseous sample for mass spectroscopy analysis is introduced into an ion resonance cell (16) within an evacuated chamber (12). An electron beam (32) is passed through the cell to ionize the gas. A magnetic field (B) is applied along a first direction within the cell and a static electric field is applied along a second direction orthogonal to the first direction. The combined action of the magnetic and static electric fields confine the ions and cause them to orbit. An alternating electric field is created within the cell to excite ions having mass-to-charge ratios within a predetermined range. A time domain signal produced by the excited ions is detected and digitized. The digital samples of the time domain electrical signal are transformed into frequency domain data by linear prediction using a linear least-squares procedure. The resultant frequency domain data contains information about the mass of the different types of ions present in the cell and the relative number of each type.