Fourier Transform Step Function [exclusive]

(it’s 0 half the time and 1 half the time), it possesses a DC component. Without this term, the transform would be incomplete and mathematically inconsistent. Why Does This Matter?

[ u(t) = \frac12 + \frac12 \textsgn(t) ] fourier transform step function

"You are 'ON' forever," the Analyst explained. "To stay 'ON' forever requires a pure, non-oscillating DC current. That is your zero-frequency part. It takes infinite energy to sustain a constant forever in a mathematical sense, hence the infinite spike." (it’s 0 half the time and 1 half

The unit step function (or Heaviside step function) is defined as: fourier transform step function

[ \int_0^\infty e^-\alpha t e^-i\omega t dt = \int_0^\infty e^-(\alpha + i\omega) t dt = \frac1\alpha + i\omega ]