General phase modulation method for stored waveform inverse Fourier transform excitation for Fourier transform ion cyclotron resonance mass spectrometry

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Abstract
A general phase modulation algorithm has been developed for the stored waveform inverse Fourier transform (SWIFT) excitation method used in Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR or FTMS). The algorithm, based on the time shifting theorem and the uncertainty principle, shows that the quadratic phase modulation is the theoretically optimal method for square magnitude spectral profiles. For more complicated magnitude spectral profiles, the corresponding phase functions can be generated through the algorithm by using a nonlinear grid on the frequency domain. The degree of dynamic range reduction can be estimated from a simple equation.