Some spectroscopic curves can be approximated by the sum of a set of component curves. For example, when Beer's law
applies, the measured intensity, I, at wavelength λ, is a linear combination of the intensity due to the individual components, k, at concentration, c. ε is an extinction coefficient. In such cases the curve of experimental data may be decomposed into sum of component curves in a process of curve fitting. This process is also widely called deconvolution. Curve deconvolution and curve fitting are completely different mathematical procedures.
Curve fitting can be used in two distinct ways.
# The line shapes and parameters  and  of the individual component curves have been obtained experimentally. In this case the curve may be decomposed using a linear least squares process simply to determine the concentrations of the components. This process is used in analytical chemistry to determine the composition of a mixture of the components of known molar absorptivity spectra. For example, if the heights of two lines are found to be h and h, c = h / ε and c = h / ε.
# Parameters of the line shape are unknown. The intensity of each component is a function of at least 3 parameters, position, height and half-width. In addition one or both of the line shape function and baseline function may not be known with certainty. When two or more parameters of a fitting curve are not known the method of non-linear least squares must be used. The reliability of curve fitting in this case is dependent on the separation between the components, their shape functions and relative heights, and the signal-to-noise ratio in the data. When Gaussian-shaped curves are used for the decomposition of set of N spectra into N curves, the  and  parameters are common to all N spectra. This allows to calculated the heights of each Gaussian curve in each spectrum (N·N parameters) by a (fast) linear least squares fitting procedure, while the  and w parameters (2·N parameters) can be obtained with a non-linear least-square fitting on the data from all spectra simultaneously, thus reducing dramatically the correlation between optimized parameters.