# 0.2 Derivation of the equations for a basic fdm-tdm transmux  (Page 5/10)

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${G}_{DFT}=\frac{2{f}_{s}QN}{M}+\frac{4C{f}_{s}N}{M}\mathrm{multiply}-\mathrm{adds}$

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 $\frac{N}{2}$ 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

${G}_{DFT}\left(N\phantom{\rule{4pt}{0ex}}\text{channels}\right)=\frac{2{f}_{s}QN}{M}+\frac{4{f}_{s}{N}^{2}}{M}.$

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 ${4}^{\frac{R}{2}}$ , 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

${G}_{\mathrm{radix}-2\phantom{\rule{4pt}{0ex}}\mathrm{FFT}}\left(\mathrm{N}\phantom{\rule{4pt}{0ex}}\mathrm{channels}\right)=\frac{2{f}_{s}N}{M}\left[Q+lo{g}_{2}N\right].$

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 $lo{g}_{2}N$ . For example, suppose that: $N=64$ for a particular problem. If more than $lo{g}_{2}64=6$ 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 $v\left(r,p\right)$ , 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.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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