This report deals with a notion of adjoint spectrum which is applicable to air-pollution monitoring by using pulsed lasers. Both Raman and absorption spectra of multiple gas complex are linear combinations of the spectra, each of which is specific to a gas species and its magnitude is proportional to the density. An extended formulation of the method of least squares is made in terms of a new notion, adjoint spectra, which visualizes the structure of the numerical filter. Applications of the derived numerical filters to the two methods are shown and features are described about the synthesized filters.