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

R w v ( j ) = lim T 1 T k = - T / 2 T / 2 w [ k ] v [ k + j ] .

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 ( · ) 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)
The correlation can be used to locate a known header within a long signal. The predefined header is shown in the top graph. The data consist of a random binary string with the header embedded and noise added. The bottom plot shows the correlation. The location of the header is determined by the peak occurring at 35.
The correlation can be used to locate a known header within a long signal. The predefined header is shown in thetop graph. The data consist of a random binary string with the header embedded and noise added. Thebottom plot shows the correlation. The location of the header is determined by thepeak occurring at 35.

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 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

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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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