<< Chapter < Page Chapter >> Page >

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

An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Elec 301 projects fall 2014. OpenStax CNX. Jan 09, 2015 Download for free at http://legacy.cnx.org/content/col11734/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elec 301 projects fall 2014' conversation and receive update notifications?

Ask