Let us assume that random binary sequence $..$mk$-$mmk$1.$ where each component mk $\{0,1\}$ is distributed by Bernoulli distribution of P$($mk $=1)=0\mathrm{.}5.$ For any k $$ N$,$ the component mk is correlated with previous symbol mk$-1$ as follows:

mk$-1$

with probability $1-$ p

Mk$=$

mk$,-1|$ with probability p

$1$

where $0<$ p $<0\mathrm{.}5.$ This sequence is sent with pulse period It$.$ Answer the following questions.

$($a$)$ Find the autocorrelation R$,$ for the impulse train of the message in discrete time. Note that the line code symbol ak is $1$ or $-1.$

$(10$ points$)$

$($b$)$ Find the PSD of the polar signaling of NRZ for pulse p$($t$)=$ I$($t$/($T$6/3)).$