# 0.5 Discussion and future work

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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 $2B<{N}^{\frac{1}{3}}$ . Thus, if a communication scheme takes at least ${2}^{14}$ samples in the time it takes to send $B=⌊\frac{1}{2}{2}^{\left(14,×,\frac{1}{3}\right)}⌋=12$ 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 $2B$ . This does not take into consideration that for any given $N$ there are

$\left(\genfrac{}{}{0pt}{}{\frac{N}{2}}{B}\right)>>{2}^{B}$

different ways to have a sparse signal of density $2B$ . 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.

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
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
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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so some one know about replacing silicon atom with phosphorous in semiconductors device?
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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.
how did you get the value of 2000N.What calculations are needed to arrive at it
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