The practical derivative deconvolution operator of the Lorentzian lineshape was obtained through approximate treatment in frequency domain. The deconvolution operator of the Voigt lineshape was obtained by convoluting the Lorentzian lineshape to the Gaussian lineshape. Applying this operator to single-and multi-lines bands in various combinations, the deconvolution spectra of the Voigt lineshape were got. It is shown that the spectral resolution enhancing factor K is related to the fraction of Lorentzian character in the combined lineshape.