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Discussion and future work

In any digital communication scheme there exist design parameters that are independent of the scheme itself: digital sampling rate and system baud rate. These parameters directly determine the values of N and B in the DMT communication scheme. It is therefore plausible to have many different values of N and B .

From the results, the FFAST algorithm outperformed the mixed-radix FFT for all signals with lengths greater than 2 14 , with the additional condition that 2 B < N 1 3 . Thus, if a communication scheme takes at least 2 14 samples in the time it takes to send B = 1 2 2 14 × 1 3 = 12 simultaneous bits, a sparse FFT will require fewer computations than the tested existing frequency domain schemes, reducing receiver bottlenecking, and will therefore be practical to use with some system designs.

Ultimately, the best way to address the viability of the sparse FFT (and therefore expand on the goals of this paper) is to physically implement a communications system compatible with the algorithm itself. While this paper has attempted to address concerns about the possibility of implementation there are still further matters to consider before a physical interpretation of this algorithm can arise.

The first and foremost matter to consider is that the version of the FFAST algorithm that we implemented only works when the signal is exactly sparse. Practically, the communications scheme would have to work with a noisy channel. A noisy version of the FFAST algorithm does exist [link] , however, and should be tested to verify our results in a noisy case.

Second, it would be useful to devise a more efficient communication scheme that takes into consideration the fact that the sparse FFT converges even though it does not“know” where the signal is not sparse. In our experiment, we allotted the first B “slots” of the frequency domain of our signal to the sinusoids, a way to guarantee that the frequency sparsity of our signal would not exceed 2 B . This does not take into consideration that for any given N there are

N 2 B > > 2 B

different ways to have a sparse signal of density 2 B . Finding a coherent way of organizing these different possibilities and using them will give transmitted signals a much higher density and also allow for a higher baud rate of the system (in the example above, B would be increased from 12 bits to 127 simultaneous bits!).

Ultimately, once these considerations are taken into account, a coherent sparse communication system seems much more plausible.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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
yes that's correct
Professor
I think
Professor
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
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
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Source:  OpenStax, Using ffast to decrease computation time in digital multitone communication. OpenStax CNX. Dec 17, 2014 Download for free at http://legacy.cnx.org/content/col11731/1.1
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