Let $f(t)$ be an even function, i.e. $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty }\:f\left ( t \right )e^{-j\omega t}dt$. Suppose $\dfrac{dF\left ( \omega \right )}{d\omega }=-\omega F\left ( \omega \right )$ for all $\omega$, and $F(0)=1$. Then
- $f\left ( 0 \right )< 1$
- $f\left ( 0 \right )> 1$
- $f\left ( 0 \right )= 1$
- $f\left ( 0 \right )= 0$