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A signal $x(t)$ has a Fourier transform $X(\omega)$. If $x(t)$ is a real and odd function of $t$, then $X(\omega)$ is

  1. a real and even function of $\omega$
  2. a imaginary and odd function of $\omega$
  3. an imaginary and even function of $\omega$
  4. a real and odd function of $\omega$

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