The Problem of Calculating the Fast-Fourier Transform of a Step-Like Sampled Function

The calculation of the fast fourier transform (FFT) for a step-like bounded function with unequal values at boundaries may be performed by using a convenient decomposition of the total curve into two elementary ones, one of them being a linear ramp. The method may be generalized to functions having asymptotic tails which may be approximated by simple analytic functions, the theoretical FFT of which is known.