Hartley transform ion cyclotron resonance mass spectrometry

Area of Science:

• Analytical Chemistry
• Spectroscopy
• Computational Science

Background:

• Ion Cyclotron Resonance (ICR) spectrometry converts time-domain signals to frequency-domain mass spectra.
• Fourier Transform (FT) is the conventional method, but requires complex variables.
• Real-valued signal processing offers computational advantages.

Purpose of the Study:

• To evaluate the Hartley transform as an alternative to the Fourier transform in ICR mass spectrometry.
• To demonstrate the advantages of using real variables in spectral analysis.
• To compare the speed and spectral output of Hartley and Fourier transforms.

Main Methods:

• Applied the Hartley transform to time-domain ICR signals.
• Compared spectral results (absorption, dispersion, magnitude modes) with Fourier transform methods.
• Utilized the discrete Fast Hartley Transform (FHT) for computational efficiency.
• Experimentally validated Hartley and Fourier transform applications in ICR mass spectrometry.

Main Results:

• The Hartley transform successfully converts ICR time-domain signals to frequency-domain mass spectra.
• Identical spectral outputs were achieved using both Hartley and Fourier transforms.
• The Fast Hartley Transform (FHT) processed data at twice the speed of a complex Fast Fourier Transform (FFT).
• The FHT demonstrated computational speed equivalent to a 'real' FFT.

Conclusions:

• The Hartley transform is a viable and advantageous alternative to the Fourier transform for ICR mass spectrometry.
• The FHT offers significant speed improvements without compromising spectral quality.
• The computational benefits of the Hartley transform are applicable to other spectroscopic techniques like NMR and IR.