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For the modulated signal $x\left ( t \right )=m\left ( t \right )\cos\left ( 2\pi f_{c}t \right )$, the message signal $m\left ( t \right )=4\cos\left ( 1000\pi t \right )$ and the carrier frequency $f_{c}$ is $1\: MHz$. The signal $x(t)$ is passed through a demodulator, as shown in the figure below. The output $y(t)$ of the demodulator is

- $\cos\left ( 460\pi t \right )$
- $\cos\left ( 920\pi t \right )$
- $\cos\left ( 1000\pi t \right )$
- $\cos\left ( 540\pi t \right )$