GATE Electrical 2014 Set 3 | Question: 35

Question

A differentiable non constant even function $x(t)$ has a derivative $y(t)$, and their respective Fourier Transforms are $X(\omega)$ and $Y(\omega)$. Which of the following statements is TRUE?

• A. $X(\omega)$ and $Y(\omega)$ are both real.
• B. $X(\omega)$ is real and $Y(\omega)$ is imaginary.
• C. $X(\omega)$ and $Y(\omega)$ are both imaginary.
• D. $X(\omega)$ is imaginary and $Y(\omega)$ is real.