Homework set 6 of ELEC 430, Rice University, Department of Electrical and
Computer Engineering
Problem 1
Consider the following modulation system
${s}_{0}(t)=A{P}_{T}(t)-1$
and
${s}_{1}(t)=-(A{P}_{T}(t))-1$
for
$0\le t\le T$ where
${P}_{T}(t)=\begin{cases}1 & \text{if $0\le t\le T$}\\ 0 & \text{otherwise}\end{cases}$
The channel is ideal with Gaussian noise which is
${}_{N}(t)=1$ for all
$t$ ,
wide sense stationary with
${R}_{N}()=b^{2}e^{-\left|\right|}$ for all
$\in \mathbb{R}$ .
Consider the following receiver structure
${r}_{t}={s}_{m}(t)+{N}_{t}$
a) Find the optimum value of the threshold for the
system (
e.g. ,
$$ that minimizes the
${P}_{e}$ ).
Assume that
${}_{0}={}_{1}$
b) Find the error probability when this threshold is used.
Problem 2
Consider a PAM system where symbols
${a}_{1}$ ,
${a}_{2}$ ,
${a}_{3}$ ,
${a}_{4}$ are transmitted where
${a}_{\mathrm{n}}\in \{2A, A, -A, -(2A)\}$ .
The transmitted signal is
${X}_{t}=\sum_{n=1}^{4} {a}_{n}s(t-nT)$
where
$s(t)$ is a rectangular pulse of duration
$T$ and height of 1. Assume that
we have a channel with impulse response
$g(t)$ which is a rectangular pulse of duration
$T$ and height 1, with white
Gaussian noise with
${S}_{N}(f)=\frac{{N}_{0}}{2}$ for all
$f$ .
a) Draw a typical sample path (realization) of
${X}_{t}$ and of the received signal
${r}_{t}$ (do not forget to add a bit of noise!)
b) Assume that the receiver knows
$g(t)$ .
Design a matched filter for this transmission system.
c) Draw a typical sample path of
${Y}_{t}$ ,
the output of the matched filter (do not forget to add a bit ofnoise!)
d) Find an expression (or draw)
$u(nT)$ where
$u(t)=(s, g, {h}^{\mathrm{opt}}(t))$ .
Problem 3
Proakis and Salehi, problem 7.35
Problem 4
Proakis and Salehi, problem 7.39
Questions & Answers
Is there any normative that regulates the use of silver nanoparticles?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?