A technique for analyzing the extended X-ray absorption fine structure spectra of an atom in different structural states in a material under study is proposed. This technique makes it possible to determine the parameters of the nearest environment of absorbing atoms without applying Fourier filtering and related techniques. The proposed approach is tested by an example of the L3 absorption spectra of platinum, obtained by direct calculation for models of one-component platinum nanoparticles and bimetallic Pt-Ag nanoparticles with different core and shell structures. The error in determining the structural parameters is analyzed, and the range of applicability of the technique proposed is discussed.