The uncertainty of the elemental analysis is one of the major factors governing the utility of on-line Prompt Gamma Neutron Activation Analysis (PGNAA) in the blending and sorting of bulk materials. In this paper, a general method applicable to Gamma spectra processing is presented and applied to PGNAA in mineral industry. Based on the Fourier transform of spectra and their de-correlation in the Fourier space (the improvement of the conditioning of the correlation matrix), processing of overlapping of characteristic peaks minimizes the propagation of random errors, which optimizes the accuracy and decreases the detection limits of elemental analyses. In comparison with classical methods based on the linear combinations of relevant regions of spectra the improvement may be considerable, especially when several elements are interfering. The method is applied to four case stories covering both borehole logging and on-line analysis on conveyor belt of raw materials. © 2009 Elsevier B.V. All rights reserved.