# 0.7 Bits to symbols to signals  (Page 5/8)

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In discrete time, cross-correlation is a function of the time shift $j$ between two sequences $w\left[k\right]$ and $v\left[k+j\right]$ :

${R}_{wv}\left(j\right)=\underset{T\to \infty }{lim}\frac{1}{T}\sum _{k=-T/2}^{T/2}w\left[k\right]v\left[k+j\right].$

For finite data records, the sum need only be accumulated over the nonzero elements, and the normalization by $1/T$ is often ignored. (This is how M atlab 's xcorr function works.) While this may look like the convolutionEquation [link] , it is not identical since the indices are different(in convolution, the index of $v\left(·\right)$ is $j-k$ instead of $k+j$ ). The operation and meaning of the two processes are also not identical:convolution represents the manner in which the impulse response of a linear system acts on its inputs to give the outputs, while cross-correlationquantifies the similarity of two signals.

In many communication systems, each message is parcelled into segments or frames, each having a predefined header.As the receiver decodes the transmitted message, it must determine where the message segments start. The followingcode simulates this in a simple setting in which the header is a predefined binary string and the data consist of a muchlonger binary string that contains the header hidden somewhere inside. After performing the correlation, the indexwith the largest value is taken as the most likely location of the header.

head=[1 -1 1 -1 -1 1 1 1 -1 -1];       % header is a predefined stringloc=30; r=25;                          % place header in position loc data=[sign(randn(1,loc-1)) head sign(randn(1,r))];  % generate signal sd=0.25; data=data+sd*randn(size(data));              % add noisey=xcorr(header, data);                 % do cross correlation [m,ind]=max(y);                        % location of largest correlation headstart=length(data)-ind+1;          % place where header starts correx.m correlation can locate the header within the data (download file) 

Running correx.m results in a trio of figures much like those in [link] . (Details will differ each time it is run, because theactual “data” are randomly generated with M atlab 's randn function.) The top plot in [link] shows the 10-sample binary header. The data vector is constructed to contain l=30 data values followed by the header (with noise added), and then $\mathtt{r}=25$ more data points, for a total block of 65 points.It is plotted in the middle of [link] . Observe that it is difficult to “see” where the headerlies among the noisy data record. The correlation between the data and the header is calculatedand plotted in the bottom of [link] as a function of the lag index. The index where the correlation attains its largest valuedefines where the best match between the data and the header occurs. Most likely this will be at index ind=35 (as in [link] ). Because of the way M atlab orders its output, the calculations represent sliding the first vector (the header),term by term, across the second vector (the data). The long string of zeroes at theend Some versions of M atlab use a different convention with the xcorr command. If you find that the string of zeros occurs at the beginning, try reversingthe order of the arguments. occurs because the two vectors are of different lengths. The start of theheader is given by length(data)-ind+1 .

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
Do somebody tell me a best nano engineering book for beginners?
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
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
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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