For a number of signals of interest, the Fourier transform integral does not converge in the usual sense of elementary calculus. Some of these signals can be treated in a consistent fashion by admitting Fourier transforms that contain impulses. For example, if , the unit-step signal, then
x(w) = (1/jω)+(πδ(ω))
For such a Fourier transform, we treat impulse components as separate in computing the magnitude spectrum since an impulse is zero at all values of but one, though admittedly something very special happens at that one point. Thus
|x(w)| = (1/ω)+(πδ(ω))