A Differential Technique for the Fourier Transform Processing of Multicomponent Exponential Functions

Abstract
Conventional Fourier transform processing of multicomponent exponential functions of the form ƒ(t) = Σ I A I e -αit commences by forming the product e x ƒ(e x ). This note is concerned with an alternative starting point-the formation of the x-derivative, ƒ ' (e x ). It is indicated that this approach: 1) yields processed outputs whose peaks are proportional to Ai directly; 2) offers an advantageously different noise performance; 3) can deal with functions containing a constant (D. C.) bias level; and 4) requires in practice only the formation of first differences.

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