Numerical deconvolution of gas chromatograph peaks using Jansson's method

Abstract

SUMMARYSeverely overlapped gas chromatographic peaks can be resolved using Jansson's method. Jansson's method is an iterative nonlinear deconvolution technique and consists of Van Cittert's algorithm with the relaxation factor a function of the kth estimate of the peak shape. The maximum peak amplitude of the instrument and peak non-negativity serve as constraints to improve the peak estimate. Super-resolution is achieved without significantly degrading the chromatogram signal-to-noise ratio. The method only requires a knowledge of the instrument impulse response function and maximum peak height.

Peak deconvolution to correctly assess the band broadening of chromatographic columns

“…The problem is discussed at length in Section 3.2.2. Some algorithms are available to reduce this signal processing artifact, such as the iterative deconvolution and the spectrum continuation [43,[64][65][66][67][68][69]. Since both methods are relatively complex, have their own limitations (relaxation or stabilization problems and peak fitting quality problems respectively) and have not shown a significant improvement in Gibbs phenomenon reduction in the peak shapes analyzed in this study, both algorithms were not further included in this work.…”

Pushing a compact 15 cm long ultra-high resolution drift tube ion mobility spectrometer with R = 250 to R = 425 using peak deconvolution

“…Therefore, special algorithms have been developed to perform this task more efficiently. One of them is the Jansson method, which was first used for the deconvolution of infrared spectra [8], but has been applied successfully to measurement data from gas chromatographs [9] and also ion mobility spectrometers [10]. It is an iterative, non-linear and constrained method with the basic algorithm given by equation (6):…”

The use of a ratio method as an alternative to constrained deconvolution

“…A chromatographic system can be modelled by the following equation: 1 -3 g = h * x + n (1) with g the observed peak data which may consist of overlapped and noisy peaks, x the ideal peak data where the peaks are fully resolved, h the system's impulse response function, n additive noise and * a convolution operator. The terms g, h, x and n are functions of time t or sequence i.…”