The invention relates to reducing harmonic signals in FT-ICR spectra. Since harmonic signals in quadrupolar 2ω-detection can be more abundant for the same ion motion in the ICR cell as compared to harmonic signals in classical dipolar 1ω-detection, they could hitherto not be reduced to satisfactory levels by any known method, such as gated deflection during ion introduction into, and correcting for an offset electric field axis in the ICR cell. The present disclosure foresees, in addition to other methods carried out for improving the measurement conditions as the case may be, performing the quadrupolar 2ω-detection at least twice, where the phase of the ion excitation radio frequency is turned by 180° in the second measurement. From the sum transient, a Fourier-transformed spectrum is derived. As a result, the broad band spectra of complex substance mixtures like crude oil become cleaner, and misinterpretations of false (harmonic) peaks are minimized.