Question $3$: Project $3$: QPSK $(20$ points$)$

A modulated QPSK symbols are $S_1,S_3,S_0,S_2,S_1.$

What is the bit stream delivered over I$-$channel and $Q-$channel, respectively?

Sketch the waveforms where $R_b=1$Mbit$\frac{s}{s}$ and $f_c=4MHz.$

A QPSK modulation can be expressed as$,$

$s(t)=b_i(t)\sqrt[\phantom{2}]{\frac{2E_b}{T_b}}cos(2f_{c}t)+b_e(t)\sqrt[\phantom{2}]{\frac{2E_b}{T_b}}sin(2f_c)$

where $b_{\text{I}}(1)=b_Q(1)=+-1.$ Calculate energy per symbol $E_s={\displaystyle \underset{0}{\overset{T_s}{}}}s(1{)}^{2}dt$ where $T_s=2T_b$

$5.$ How to retrieve $b_1(t)$ and $b_Q(t)$ for QPSK$,$ mathematically