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

 Page 5 / 8

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 .

#### Questions & Answers

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
Got questions? Join the online conversation and get instant answers!