# 0.7 Bits to symbols to signals  (Page 3/8)

 Page 3 / 8

A Gray code has the property that the binaryrepresentation for each symbol differs from its neighbors by exactly one bit.A Gray code for the translation of binary into 4-PAM is

$\begin{array}{ccc}01\hfill & \to \hfill & +3\hfill \\ 11\hfill & \to \hfill & +1\hfill \\ 10\hfill & \to \hfill & -1\hfill \\ 00\hfill & \to \hfill & -3\hfill \end{array}$

Mimic the code in naivecode.m to implement this alternative and plot the number of errors as a function ofthe noise variance v . Compare your answer with [link] . Which code is better?

## Symbols to signals

Even though the original message is translated into the desired alphabet, it is not yet ready for transmission:it must be turned into an analog waveform. In the binary case, a simple method is to use a rectangular pulseof duration $T$ seconds to represent $+1$ , and the same rectangular pulse inverted (i.e., multiplied by $-1$ ) to represent the element $-1$ . This is called a polar non-return-to-zero line code.The problem with such simple codes is that they use bandwidth inefficiently.Recall that the Fourier transform of the rectangular pulse in time is the $\text{sinc}\left(f\right)$ function in frequency [link] , which dies away slowly as $f$ increases. Thus, simple codes like the non-return-to-zeroare compact in time, but wide in frequency, limiting the number of simultaneous nonoverlapping users ina given spectral band.

More generally, consider the four-level signal of [link] . This can be turned into an analog signal for transmission by choosinga pulse shape $p\left(t\right)$ (that is not necessarily rectangular and not necessarily of duration $T$ ) and then transmitting

$\begin{array}{cc}\hfill p\left(t-kT\right)& \text{if}\phantom{\rule{4.pt}{0ex}}\text{the}\phantom{\rule{4.pt}{0ex}}k\text{th}\phantom{\rule{4.pt}{0ex}}\text{symbol}\phantom{\rule{4.pt}{0ex}}\text{is}\phantom{\rule{4.pt}{0ex}}1\hfill \\ \hfill -p\left(t-kT\right)& \text{if}\phantom{\rule{4.pt}{0ex}}\text{the}\phantom{\rule{4.pt}{0ex}}k\text{th}\phantom{\rule{4.pt}{0ex}}\text{symbol}\phantom{\rule{4.pt}{0ex}}\text{is}\phantom{\rule{4.pt}{0ex}}-1\hfill \\ \hfill 3p\left(t-kT\right)& \text{if}\phantom{\rule{4.pt}{0ex}}\text{the}\phantom{\rule{4.pt}{0ex}}k\text{th}\phantom{\rule{4.pt}{0ex}}\text{symbol}\phantom{\rule{4.pt}{0ex}}\text{is}\phantom{\rule{4.pt}{0ex}}3\hfill \\ \hfill -3p\left(t-kT\right)& \text{if}\phantom{\rule{4.pt}{0ex}}\text{the}\phantom{\rule{4.pt}{0ex}}k\text{th}\phantom{\rule{4.pt}{0ex}}\text{symbol}\phantom{\rule{4.pt}{0ex}}\text{is}\phantom{\rule{4.pt}{0ex}}-3\hfill \end{array}$

Thus, the sequence is translated into an analog waveform by initiating a scaled pulse at the symbol time $kT$ , where the amplitude scaling is proportional to the associated symbolvalue. Ideally, the pulse would be chosen so that

• the value of the message at time $k$ does not interfere with the value of the message at other sample times(the pulse shape causes no intersymbol interference ),
• the transmission makes efficient use of bandwidth, and
• the system is resilient to noise.

Unfortunately, these three requirements cannot all be optimized simultaneously, and so the design of thepulse shape must consider carefully the tradeoffs that are needed. The focus in Chapter [link] is on how to design the pulse shape $p\left(t\right)$ , and the consequences of that choice in terms of possible interference betweenadjacent symbols and in terms of the signal-to-noise properties of the transmission.

For now, to see concretely how pulse shaping works, let's pick a simple nonrectangular shape and proceedwithout worrying about optimality. Let $p\left(t\right)$ be the symmetrical blip shape shown in the top part of [link] , and defined in pulseshape.m by the hamming command. The text string in str is changed into a 4-level signal as in Example [link] , and then the complete transmitted waveform is assembled by assigning an appropriatelyscaled pulse shape to each data value. The output appears in the bottom of [link] . Looking at this closely, observe that the first letter T is represented by the four values $-1\phantom{\rule{4pt}{0ex}}-1\phantom{\rule{4pt}{0ex}}-1\phantom{\rule{4pt}{0ex}}-3$ , which corresponds exactly to the first four negative blips, three small and one large.

what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!