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Text to binary conversion

The first step is to convert our information into binary. We used the sentence “hello, this is our test message,” repeated four times, as our text message. To get it into binary, we used standard ASCII text mapping.

hello = 01101000 01100101 01101100 01101100 01101111

Series to parallel

The next step is converting this vector of zeros and ones into a matrix. The vector is simply broken up into blocks of length L, and each block is used to form column of the matrix.

Constellation mapping

Now the fun begins. The primary method of modulation in DMT is by inverse Fourier Transform. Although it may seem counterintuitive to do so, by taking the inverse Fourier Transform of a vector or a matrix of vectors, it effectively treats each value as the Fourier coefficient of a sinusoid. Then, one could transmit this sum of sinusoids to a receiver that would in turn take the Fourier Transform (the inverse transform of the inverse transform, of course) and retrieve the original vectors.

But instead of taking the transform of our vectors of zeros and ones, we first convert bit streams of length B to specific complex numbers. We draw these complex numbers from a constellation map (a table of values spread out along the complex plane). See the figure below for an example of a 4 bit mapping.

Constellation mapping table

const map
This table shows which bit stream is mapped to which complex value.

Signal mirroring and inverse fourier transform

Why would we do that, you might ask. Doesn’t converting binary numbers to complex ones just make things more complicated? Well, DMT utilizes the inverse Fourier Transform in order to attain its modulation. So taking the IFFT of a vector of complex numbers will result in a sum of sinusoids, which are great signals to be sending over any channel (they are the eigenfunctions of linear, time-invariant systems).

But before taking the inverse transform, the vectors/columns of the matrix must be mirrored and complex conjugated. The Inverse Fourier Transform of a conjugate symmetric signal results in a real signal. And since we can only transmit real signals in the real world, this is what we want.

Cyclic prefix

If we were transmitting over an ideal wire system, we would be done at this point. We could simply send it over the line and start demodulating. But with most channels, especially our acoustic one, this is not the case. The channel’s impulse response has non-zero duration, and will therefore cause inter-symbol interference in our output.

Intersymbol interference occurs during the convolution of the input and impulse response. Since the impulse response has more than a single value length, it will thus cause one block’s information to bleed into the next one.

To prevent this, we added what is called a cyclic prefix to each block. As long as the length of the cyclic prefix is at least as long as the impulse response, it should prevent ISI. However, it has a secondary effect as well. We created the prefix by adding the last N values of each block (where N is the length of the response) to the beginning, preserving the order. Doing this effectively converts the linear convolution of the impulse response with the block sequence to circular convolution with each block separately, since there will now be the “wrap-around” effect. This will be handy later when we start characterizing the channel, since circular convolution in time is equivalent to multiplication of DFT’s in frequency.

00010110011010001 =>01000100010110011010001

The first six bits in the second bit stream, 010001, is the cylcic prefix. Note that although these values are binary, they could essentially range from -1 to 1 since they sample the sinusoid sum that was formed after inverse Fourier Transforming.

Please see the block diagram below. It summarizes the entire transmission process covered above.

Transmission block diagram

Transmission block diagram.
This diagram shows the all of the components and flow of our transmission system.

Questions & Answers

what is the VA Ha D R X int Y int of f(x) =x²+4x+4/x+2 f(x) =x³-1/x-1
Shadow Reply
can I get help with this?
Wayne
Are they two separate problems or are the two functions a system?
Wilson
Also, is the first x squared in "x+4x+4"
Wilson
x^2+4x+4?
Wilson
thank you
Wilson
Please see ***imgur.com/a/lpTpDZk for solutions
Wilson
f(x)=x square-root 2 +2x+1 how to solve this value
Marjun Reply
factor or use quadratic formula
Wilson
what is algebra
Ige Reply
The product of two is 32. Find a function that represents the sum of their squares.
Paul
if theta =30degree so COS2 theta = 1- 10 square theta upon 1 + tan squared theta
Martin Reply
how to compute this 1. g(1-x) 2. f(x-2) 3. g (-x-/5) 4. f (x)- g (x)
Yanah Reply
hi
John
hi
Grace
what sup friend
John
not much For functions, there are two conditions for a function to be the inverse function:   1--- g(f(x)) = x for all x in the domain of f     2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the  element that you started with, namely, x.
Grace
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
acha se dhek ke bata sin theta ke value
Ajay
sin theta ke ja gha sin square theta hoga
Ajay
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
False statement so you cannot prove it
Wilson
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
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Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
comment écrire les symboles de math par un clavier normal
SLIMANE
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
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.
Ramkumar Reply
what is nano technology
Sravani Reply
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, Discrete multi-tone communication over acoustic channel. OpenStax CNX. Dec 16, 2009 Download for free at http://cnx.org/content/col11146/1.1
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