Resolution in Fourier spectra can be significantly enhanced by displaying magnitudes of the complex peak derivatives with respect to frequency. These derivatives are computed by the judicious application of a new kind of windows, which reduce peak widths. When thus sharpened peaks are purely Lorentzian, then simple linear or parabolic regressions allow one to compute their parameters. A Fourier-transform ion cyclotron resonance mass spectrometric example of such an improvement is presented.Fourier spectrometries are based on Fourier transform (FT) analysis of temporal responses of physical systems to convenient pulses.'-3 Despite their numerous advantages, they however exhibit some well-known drawbacks (broad overlapping peaks; difficulties of estimating parameters, etc.). We have developed new classes of windows, both derivatizing and apodizing, which allow resolution enhancement and parameter computation. These windows have been efficiently applied in the field of NMR. We want to show that they may also be used in that of mass spectrometry.
SOME DRAWBACKS OF FOURIER TRANSFORM (FT) METHODSI T spectra drawbacks may be due either to computational ways of calculation,'-' or to the FT principle itself.Computation shortcomings are related both to data sampling and to fast computation processes (FFT), which limit the acquisition time and the computation width, thus creating a transient cut-off. FT are then characterized by the existence of spurious oscillations, known as the Gibbs phenomenon, and folding of spectra.'-' Moreover, calculations of Fourier integrals as sums of series lead to numerical discrepancies, especially in phase determination^.^ It is possible to limit some of these disadvantages through a convenient temporal signal processing before Fourier transformation. Thus, we may increase the number of computation points, choose correct sampling time intervals and apply weighting windows (named apodization windows in optics), which reduce both Gibbs oscillations and noise.In addition to these shortcomings, specific to the sampling process, the Fourier transform of exponentially damped transients itself presents an additional one, related to peak structures. To illustrate it, let us suppose that the transient response is made up of a linear sum of K damped oscillating complex exponentials.To avoid a transient cut-off and the Gibbs phenomenon, we can apply an exponential weighting window A, being the amplitudes, u k the angular frequencies, A k = l/tk the damping factors, @k the phases at origin, and j the base of complex numbers. After having set the first sample ( t = 0 ) to its half value, in order to avoid a spectral baseline offset, the spectrum equation is:Far from o = wk, each component of this sum is characterized by a broad magnitude peak varying as (o -ok)-'. The consequence is that, when displayed together, two close components may overlap, which leads to severe artefacts when the phases @k are not identical .6
