0.7 Bits to symbols to signals  (Page 2/8)

 Page 2 / 8
$...000010110101...\to ...00\phantom{\rule{4pt}{0ex}}00\phantom{\rule{4pt}{0ex}}10\phantom{\rule{4pt}{0ex}}11\phantom{\rule{4pt}{0ex}}01\phantom{\rule{4pt}{0ex}}01....$

Then the pairs might be encoded as

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

to produce the symbol sequence

$...00\phantom{\rule{4pt}{0ex}}00\phantom{\rule{4pt}{0ex}}10\phantom{\rule{4pt}{0ex}}11\phantom{\rule{4pt}{0ex}}01\phantom{\rule{4pt}{0ex}}01...\to ...-3,\phantom{\rule{4pt}{0ex}}-3,\phantom{\rule{4pt}{0ex}}+1,\phantom{\rule{4pt}{0ex}}+3\phantom{\rule{4pt}{0ex}},-1,\phantom{\rule{4pt}{0ex}}-1....$

Of course, there are many ways that such a mapping between bits and symbols might be made, and [link] explores one simple alternative called the Gray code.The binary sequence may be grouped in many ways: into triplets for an 8-level signal, intoquadruplets for a 16-level scheme, into “in-phase” and “quadrature” parts for transmission through aquadrature system. The values assigned to the groups ( $±1,±3$ in (8.2)) are called the alphabet of the given system.

Text is commonly encoded using ASCII, and M atlab automatically represents any string file as a list of ASCII numbers.For instance, let str='I am text' be a text string. This can be viewed in its internal form bytyping real(str) , which returns the vector $73\phantom{\rule{4pt}{0ex}}32\phantom{\rule{4pt}{0ex}}97\phantom{\rule{4pt}{0ex}}109\phantom{\rule{4pt}{0ex}}32\phantom{\rule{4pt}{0ex}}116\phantom{\rule{4pt}{0ex}}101\phantom{\rule{4pt}{0ex}}120\phantom{\rule{4pt}{0ex}}116$ , which is the (decimal) ASCII representation of this string.This can be viewed in binary using dec2base(str,2,8) , which returns the binary (base 2) representation of thedecimal numbers, each with 8 digits.

The M atlab function letters2pam.m , provided on the website,changes a text string into the 4-level alphabet $±1,±3$ . Each letter is represented by a sequence of 4 elements, for instance the letter $I$ is $-1\phantom{\rule{4pt}{0ex}}-3\phantom{\rule{4pt}{0ex}}1\phantom{\rule{4pt}{0ex}}-1$ . The function is invoked with the syntax letters2pam(str) . The inverse operation is pam2letters.m . Thus pam2letters(letters2pam(str)) returns the original string.

One complication in the decoding procedure is that the receiver must figure out when the groups begin in order to parse thedigits properly. For example, if the first element of the sequence in [link] was lost, then the message would be mistranslated as

$\begin{array}{ccc}\hfill ...00010110101...& \to & ...00\phantom{\rule{4pt}{0ex}}01\phantom{\rule{4pt}{0ex}}01\phantom{\rule{4pt}{0ex}}10\phantom{\rule{4pt}{0ex}}10...\hfill \\ & \to & ...-3,\phantom{\rule{4pt}{0ex}}-1,\phantom{\rule{4pt}{0ex}}-1,\phantom{\rule{4pt}{0ex}}1,\phantom{\rule{4pt}{0ex}}1,....\hfill \end{array}$

Similar parsing problems occur whenever messages start or stop. For example, if the message consistsof pixel values for a television image, it is important that the decoder be able to determine precisely when the image scan begins. These kinds of synchronization issues are typically handledby sending a special “start of frame” sequence that is known to both the transmitter and the receiver.The decoder then searches for the start sequence, usually using some kind of correlation (pattern matching) technique.This is discussed in detail in "Correlation" .

There are many ways to translate data into binary equivalents. Example  "Bits to Symbols" showed one way to convert text into 4-PAM and then into binary. Another way exploits theM atlab function text2bin.m and its inverse bin2text.m , which use the 7-bit version of the ASCII code (rather than the 8-bit version). This representationis more efficient, since each pair of text letters can be represented by 14 bits (or seven 4-PAM symbols) rather than16 bits (or eight 4-PAM symbols). On the other hand, the 7-bit version can encode only half as many charactersas the 8-bit version. Again, it is important to be able to correctly identify the start of each letterwhen decoding.

The M atlab code in naivecode.m , which is on the website, implements the translation from binary to 4-PAM(and back again) suggested in [link] . Examine the resiliency of this translation to noiseby plotting the number of errors as a function of the noise variance v . What is the largest variance for which no errors occur? At what varianceare the errors near 50%?

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
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Abhi
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salma
Commplementary angles
Idrissa Reply
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Sherica
im all ears I need to learn
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Tamia
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Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
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a perfect square v²+2v+_
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
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rolling four fair dice and getting an even number an all four dice
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Kristine 2*2*2=8
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Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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China
Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
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what is nano technology
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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