In an ion cyclotron resonance mass spectrometer ions are excited into cyclotron orbits by an alternating current excitation signal having a nonlinear function of the excitation frequency vs. time in a “chirp.” Such an excitation signal produces transients which have no pronounced beats, even if mixtures of many ion species, all having the same mass differences, are present. The dynamic measuring range for the image currents can thus be better utilized. In particular, sum spectra of specified quality can be generated from a significantly smaller number of individual transients, and thus in a significantly shorter measuring time.