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

Conventional Fourier transform processing of multicomponent exponential functions of the form f(t) = ¿iAie-¿it commences by forming the product exf(ex). This note is concerned with an alternative starting point¿the formation of the x-derivative, f´(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.