Use of the filter diagonalization method in the study of space charge related frequency modulation in Fourier transform ion cyclotron resonance mass spectrometry

Abstract

The filter diagonalization method (FDM) is a recently developed computational technique capable of extracting resonance frequencies and amplitudes from very short transient signals. Although it requires stable resonance frequencies and is slower than the fast Fourier transform (FFT), FDM has a resolution and accuracy that is unmatched by the FFT or any other comparable techniques. This unique feature of FDM makes it an ideal tool for tracing space charge induced frequency modulations in Fourier transform ion cyclotron resonance (FT-ICR) cells, which are shown to reach +/-400 ppm even for such simple spectra as Substance P.

Towards analytically useful two-dimensional Fourier transform ion cyclotron resonance mass spectrometry

“…We are also looking into possibilities offered by alternative pulse sequences, especially by adapting ideas such as the accordion experiment [64] from 2D NMR spectroscopy to 2D FT-ICR MS which may give access to the ion lifetime. We can also obtain highresolution 2D mass spectra through alternative data processing methods, such as the filter diagonalization method, which shows great promise in 1D FT-ICR MS [14,65].…”

High-Resolution and Tandem Mass Spectrometry – the Indispensable Tools of the XXI Century

“…A number of groups, including ours, are in the process of tailoring super-resolution signal processing methods, e.g. the filter diagonalization method (FDM), to the needs of the ICR and Orbitrap MS. [48] The goal is to replace FT-based signal processing with methods that would require 10-100 times shorter transient time-domain signals to yield a similar level of resolving power. In the distant future this may allow the next important step in resolving power increase to be made that could enable the differentiation between the isomers of a given molecule, which is not achievable today.…”

The spontaneous loss of coherence catastrophe in fourier transform ion cyclotron resonance mass spectrometry

“…Frequency shifts due to space-charge were reported to be greater than ±400 ppm within an isotopic beat [20], which affects both position and width of the peaks, although these periodic shifts tend to mostly average out over a long transient. Substantial effort has been invested and there have been previous attempts to study it in situ [21, 22], yet the phenomenon remains poorly studied due to its rather fast nature, which requires frequency shift analysis on very short segments of transient signals.…”

“…The filter diagonalization method (FDM) [31-39] is a recent addition [20] to the repertoire of computational techniques in mass spectrometry, which addresses these issues. Like the FFT, it finds a solution for the generic harmonic inversion problem [37] (HIP) eq 1, $$\mathcal{C}\left(t_n\right)=c_n\equiv \sum _{k=1}^K{d}_k{e}^{-in\tau \omega k},$$ where the d k ’s and ω k ’s are complex amplitudes and complex frequencies respectively, and C ( t n ) is a time signal defined on an equidistant time grid t n = nτ , n = 0,1, .…”