Resolution of partially overlapped signals by Fourier analysis. Application to differential-pulse polarographic responses

Abstract

An analysis of the first harmonic components of the sequence resulting from a suitable deconvolution operation on a response composed of single partially overlapped signals allows the resolution of the over-all response into the individual signals. Ideally, it is possible to reduce the original response to single impulses with suitable height and location. If the number, n, of single signals is known, the first n– 1 harmonic components of the spectrum of the deconvoluted response, plus the continuous term, need only be computed. On the other hand, if the over-all response includes an unknown number of single signals, a method is suggested that requires the calculation of only a few harmonic components in order to build up a suitable form of the whole spectrum of the deconvoluted signal. The effectiveness of the proposed procedures, which are suitable for the treatment of responses from different analytical techniques, was tested on simulated responses, both in the absence and presence of noise, and on experimental data, viz., differential-pulse polarographic responses recorded on solutions containing two metals that were reduced at similar potentials.