Williams C P, Marshall A G
Anal Chem. 1989 Mar 1;61(5):428-31. doi: 10.1021/ac00180a010.
The Hartley transform offers a useful alternative to the Fourier transform for the conversion of a time-domain ion cyclotron resonance (ICR) signal into its corresponding frequency-domain mass spectrum. The Hartley transform has the advantage that it eliminates the need for complex variables, when (as for linearly polarized signals) the time-domain signal can be represented by a mathematically real function. Moreover, the Hartley transform produces the same spectra (absorption mode, dispersion mode, magnitude mode) as does the Fourier transform. In particular, the discrete fast Hartley transform (FHT) produces the same spectrum at twice the speed of a complex fast Fourier transform (FFT), making the FHT equivalent in speed to a "real" FFT. Hartley and Fourier transform methods in ICR mass spectrometry are compared and demonstrated experimentally. Essentially the same advantages and computational methods should apply to the use of the Hartley transform in place of the Fourier transform in other forms of spectrometry (e.g., nuclear magnetic resonance, infrared, etc.).
