Discrete Fourier transform techniques for noise reduction and digital enhancement of analytical signals

Abstract

Comprehensive details of problem solving approaches with discrete Fourier transform (DFT) are presented with reference to current separation science applications, which are equally applicable to spectroscopic data. A super-Gaussian window in DFT allows denoising without broadening the peaks, unlike the standard time domain digital filters. DFT deconvolution is shown to remove extra-column effects on a 3 cm column leading to a significant increase in theoretical plates and reduced asymmetry. Twin-column recycling HPLC is an ultrahigh-resolution technique that can resolve isotopically labeled compounds. The concept of Fourier self-deconvolution is demonstrated for virtual resolution of deuterated benzenes’ chromatogram using a twin-column recycling HPLC. Higher order derivatives of noisy signals are readily calculated and denoised by the DFT filter. Fourier deconvolution, approximated as a series sum of derivatives allows symmetrization of tailing Gaussians (or any function convoluted with an exponential function). Peaks buried under the tail even with an area ratio of 100:1 can be exposed. A comparison of Fourier self-deconvolution is provided with other numerical methods such as power law, van Cittert, iterative curve fitting, and first derivative methods for a highly overlapped signal.