A novel method for processing of periodic signals, which combines absorption spectra presentation with magnitude spectra and finite-impulse-response filtering, is applied to image current transients acquired in Orbitrap mass spectrometry. Phasing of signal for absorption spectra is facilitated by the excitation-by-injection mechanism of forming coherent ion packets in the Orbitrap analyzer. In conjunction with extensive refinement of the trap and electronics design of the Orbitrap analyzer, this method allows completion of the excitation process and initiation of detection within a fraction of a millisecond after ejection of ions from an external storage device into the Orbitrap analyzer, thus avoiding baseline roll and large non-linear phase corrections. For most real-life analytes with limited signal decay over acquisition time, the method achieves a 2-fold increase of resolving power relative to the traditional Fourier transform processing method. For rapidly decaying signals of intact proteins, the relative increase in resolving power is reduced to about 1.4, which accords with theory. Peak shape and mass accuracy in LC/MS measurements obtained employing the novel method appear to be similar to those observed in traditional magnitude-mode FT spectra. Performance of the method was optimized using calibration mixtures and tested on different real-life samples, including complex peptide mixtures and proteins supplied to the mass spectrometer in infusion and LC/MS modes.