6. Consider a double sideband system with quadrature multiplexing (QM) which simultaneously sends two messages \( m_{1}(t) \) and \( m_{2}(t) \) through \( \cos 2\pi f_{c}t \) and \( \sin 2\pi f_{c}t \), respectively. The transmitted signal is given by

$$x(t) = A[m_1(t) \cos 2\pi f_c t + m_2(t) \sin 2\pi f_c t].$$

(a)(10%) Suppose the phase is perfectly known to the receiver and there is no noise, design a coherent demodulator that can recover both the messages. You must show that the demodulator can correctly demodulate.