Resolution enhancement of spectra using differentiation

The problem of determination of positions and heights of the spectral lines was analyzed using a numerical differentiation procedure. The deconvolution method provided best starting values for the positions of the lines for the nonlinear fitting methods. By modeling the spectra as probability measures in an appropriate Hilbert space framework, estimates were derived that characterized the nature of the smoothing performed by the regularization recovery methodology proposed. The examination of the trade-off between resolution and the various types of error that occur in a measured spectrum using Hilbert space framework was also presented.