A differentiable non-constant even function x(t) has a derivative

Home » Signals and Systems » Signals and systems electrical engineering miscellaneous » Question

A differentiable non-constant even function x(t) has a derivative y(t), and their respective Fourier Transforms ar e X(ω) and Y(ω). Which of the following statements is TRUE?

1. X(ω) and Y(ω) are both real.
2. X(ω) is real and Y(ω) is imaginary.
3. X(ω) and Y(ω) are both imaginary.
4. X(ω) is imaginary and Y(ω) is real.

Correct Option: B

y(t) =	d	x(t)
	dt

Y(ω) = jω × (ω)
⇒ if X(ω) is real, Y(ω) is imaginary