Prove that the Fourier transform of the unit-step signal, u(t), iswhere K = π. At first gl...

Prove that the Fourier transform of the unit-step signal, u(t), is

where K = π. At first glance, it might seem that the impulse term Kδ(ω) should be zero, but show that K ≠ 0 because the following signal s(t) is an odd symmetric signal.

Note: Even though S(t) and u(t)  differ at one isolated point, t = 0, they still have the same Fourier transform