A digital technique for analyzing a class of multicomponent signals

There are numerous occasions in applied sciences where there is need to analyze multicomponent signals formed by a linear superposition of functions having the same shape and location but different widths and amplitudes. A fast digital technique capable of producing the spectrum, i.e., the distribution of component amplitudes versus component widths, of such experimental data is presented in this paper. The method described does not require any a priori numerical information regarding the composition of the signal, can be easily and efficiently implemented on digital computers, can be automated, and is essential for an automated interpretation of these types of laboratory data. The technique is based upon a nonlinear change of variables followed by a deconvolution. A low-pass filtering is necessary in the final stage of data processing to reduce the effect of computational and experimental noise. As a main example of the practical implementation of this technique within a laboratory environment, the paper details its usage in connection with pulsed NMR measurements on malignant tissues, where the data have the form of a superposition of exponential decays.