Reference deconvolution in the frequency domain.

Abstract

Reference deconvolution, i.e., using the lineshape distortions of a reference signal with known ideal shape to deduce a correction function for the whole spectrum, is normally performed in the time domain. As a disadvantage, reference signals of higher multiplicity cannot be employed because of mathematical instabilities. In this work we show that these difficulties can be circumvented by carrying out reference deconvolution in the frequency domain. The computational demands of this approach are higher, but not prohibitive, because the width of the correction function is only a fraction of that of the whole spectrum. An iterative algorithm was implemented that yields the optimum widths of the correction function and of the ideal reference signal. Singular value decomposition was found to produce better results than LU decomposition of the design matrix. The feasibility of the deconvolution method and of the algorithm are demonstrated using both synthetic and experimental data.