CHAT GPT PROHIBITED

Problem $4)[20$pt$]$ A radio station broadcasts $N$ different music programs $m_n(t)$ simultaneously,

as depicted in the diagram below.

Figure $2$: Diagram of radio station transmitter

Assume that the entire communication system is noiseless.

$($a$)[5$pt$]$ What is the condidtion for bandwidth of each raido program $m_n(t)$ to prevent interfer$-$

ence from the different programs?

$($b$)[5$pt$]$ Jane wants to listen to the radio program $m_1(t).$ Draw a block diagram of Jane's radio

to extract $m_1(t).$

$($c$)[5$pt$]$ Explain the receiver processing of Jane's radio in the frequency domain perspective.

Assume that all programs are of the form $m_n(t)=\frac{sin(200t)}{t},$ and the phase of the demodulator

is set to $0.($meaning that there is no phase error$)$

$($d$)[5$pt$]$ Unfortunately, Jane's radio is broken and thus unintended phase shift is introduced in

the demodulator. Explain why this poses a problem using mathematical expressions.