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

Conventional Fourier transform processing of multicomponent exponential functions of the form ƒ(t) = ΣIAIe-αitcommences by forming the product exƒ(ex). This note is concerned with an alternative starting point-the formation of the x-derivative, ƒ'(ex). 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.