RESOLUTION OF MULTI‐COMPONENT EXPONENTIAL DECAY CURVES USING FOURIER TRANSFORMS

Abstract

Abstract A frequently encountered problem in many branches of science involves the resolution of experimental data in a sum of exponentials of the form image to estimate the physically significant parameters Ni° and λ i and to determine n, the number of components. The components may be separate and unrelated, or there may be decay chains where some components are produced as the result of the disappearance of other components. In the present approach the exponential series is represented by a Laplace integral equation image . This equation is inverted by a method of Fourier transforms. The results of the analysis appear in the form of a frequency spectrum. Each true peak in the spectrum indicates a component, the abscissa value at the center of the peak is the decay constant λi while the height of the peak is directly proportional to Ni°/λi.