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G D F T = 2 f s Q N M + 4 C f s N M multiply - adds

are needed for the preprocessor/DFT method.

The goal outlined in the section "What is an FDM-TDM Transmultiplexer" was to demultiplex all of the channels carried in the input FDM signal. If the input sampling rate is not chosen extravagantly, then the number of channels should be somewhat less than N 2 if the input signal is real-valued, and somewhat less than N if the signal is complex-valued. To obtain the worst-case situation, we assume that it is complex-valued and that C = N . In this case, the total multiply-add computation is given by

G D F T ( N channels ) = 2 f s Q N M + 4 f s N 2 M .

Even though this value is less than that required by the direct tuning method, the quadratic dependence on the number of channels N makes this method expensive for situations where a large number of channels must be dealt with.

Solution to this problem comes in the form of the fast Fourier transform (FFT), a class of algorithms that can be used to efficiently compute all of the points of a DFT if N the size of the DFT, meets certain conditions. In particular, if N is a so-called highly composite number that is, it is the product of small positive integers, then various symmetries can be exploited to dramatically reduce the computation needed to compute the desired C tuner outputs.

In practice the size of the DFT, N , is typically chosen to equal 2 R or 4 R 2 , where R is some positive integer, resulting in what is known as the radix-2 or radix-4 FFT, respectively An important exception to this is the so-called prime-factor transform in which N is the product of small, prime factors (e.g., 2, 3, 5 , 7, 11, etc). .

For discussion here we will assume the use of a radix-2 FFT (even though it is well known that the radix-4 algorithm is somewhat more computationally efficient). With this assumption we find that the number of multiply-adds needed to compute all N possible tuner outputs, is given by

G radix - 2 FFT ( N channels ) = 2 f s N M [ Q + l o g 2 N ] .

Comparison of this equation with [link] shows that the FFT-based method always requires less computation than direct DFT computation of all N tuners and requires less than the direct DFT computation of C tuners when C exceeds l o g 2 N . For example, suppose that: N = 64 for a particular problem. If more than l o g 2 64 = 6 tuners are required, then the FFT is more efficient. If C is more on the order of 50, as it probably would be, then FFT-based computation of the DFT is about eight times more efficient than direct computation of the DFT and even more efficient compared to conventional computation of the tuner outputs. A graphical example is shown in [link] .

The generic FFT-based transmultiplexer consists of a preprocessor, which blocks, weights, and sums the input data to produce the N values of v ( r , p ) , and an FFT, which efficiently computes the DFT for every value of n . This structure is shown in [link] . The input data is sampled (or provided by a preceding digital subsystem), preprocessed, and DFTed using the FFT algorithm. The FFT output bins are read out sequentially, thus producing the time division multiplexed (TDM) form promised originally.

Questions & Answers

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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
Devang Reply
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
Abhijith Reply
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
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, An introduction to the fdm-tdm digital transmultiplexer. OpenStax CNX. Nov 16, 2010 Download for free at http://cnx.org/content/col11165/1.2
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