Question $3(10$ marks$)$

$($a$)$ Suppose a baseband audio signal which has a frequency range of $0$ to $16$ kHz $,$ is amplitude modulated with a carrier wave of $200$ kHz $.$

$($i$)$ Determine the frequency range and the centre frequency of the amplitude modulated signal.

$($ii$)$ What will happen to the amplitude of the audio signal after amplitude modulation?

$($b$)$ Given a carrier signal $c(t)$ as below and consider a message signal $m(t)=500+300sin(4000t).$

$($i$)$ Sketch the time domain representation of $m(t)$ and the amplitude modulated signal $s_a(t)$ for the first $0\mathrm{.}002$ s in the same graph. The carrier frequency within the modulated signal can be roughly sketched. Clearly label the times and amplitudes.

$($ii$)$ Sketch the frequency modulated signal $s_f(t)$ from $m(t)$ for the first $0\mathrm{.}002$ s $.$ The carrier frequency within the modulated signal can be roughly sketched. But the characteristics of frequency modulation must be clearly shown. Clearly label the times and amplitudes.

Question $4(7$ marks$)$

A CDMA signal $s(t)$ is received as shown below,

Assume all messages being sent through $s(t)$ are $2$ bits long. Decode the messages $m_1$ and $m_2$ encrypted in $s(t)$ by using the Walsh$-$Hadamard Code $w_1=\left[\begin{array}{cccccc}1& 0& 0& 1& 0& 1\end{array}\right]$ all your calculation steps clearly.