Consider the quadrature-carrier multiplex system of Figure. The multiplexed signal s (t) produced at the transmitter output in Figure a is applied to a communication channel of frequency response H (ƒ). The output of this channel is, in turn, applied to the receiver input in Figure b. Prove that the condition H (ƒ_c + ƒ) = H* (ƒ_c – ƒ), 0 < ƒ < W is necessary for recovery of the message signals m₁ (t) and m₂ (t) at the receiver outputs; ƒ_c is the carrier frequency, and W is the message bandwidth.