<< Chapter < Page Chapter >> Page >
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 housing
Baldwin Reply
Blood in Pulmonary artery
Deepa Reply
why can't I open the link
Kravin Reply
how does hormones produce in our body
Shubham Reply
what is an organelle
Shemia Reply
it is the membranious componet within a cell... eg mitochondrion
Joseph
what is the Endothelial cell?
Jumana Reply
classification of heart
NARESH Reply
classification of heart 5 points
NARESH
wow
Ashley
wym by classification?
Ashley
differences between meiosis and mitosi
Daniel Reply
how much function it have
Kerlon Reply
what is a cell membrane
Kerlon
call membrane is outer most part of cell
PRIYA
cell membrane consists from phospholipids and proteins
Jumana
what is elastic constant in muscle in human of body
which topic you at now
Jodyann
Cells
david
what is chromosome
jeff Reply
a thread-like structure of nucleic acids and protein found in the nucleus of most living cells, carrying genetic information in the form of genes
Niola
what are the medical application of hooks law experiment in human body
what is the physical reason that make people get fractured in bones or rupture of tissues
Hooke's Law is the Law of Elasticty. In scientific terms, Hooke's Law is the displacement or size of the deformation is directly proportional to the deforming force or load. Under these conditions the object returns to its original shape and size upon removal of the load
Niola
what is DNA
abdala
deoxyribonucleic acid, a self-replicating material which is present in nearly all living organisms as the main constituent of chromosomes. It is the carrier of genetic information.
Niola
what is prokaryotic cell
Farid
greetings
Nsoh
am Modesta
Nsoh
what is deamination
Mohamed
what is defusion
Rashima Reply
diffusion is the movement of molecules from a region of higher concentration to a region of lower concentration through a permeable membrane
Dein-aboh
and osmosis is the same thing ?
Rashima
nope
Ashley
The spreading of something more widely
R0se
Osmosis is the movement of water molecules from a region of higher concentration to a region of lower concentration
Lavern
What is a color of blood before it is exposed to oxygen?
Lavern
hello there....I have a problem concerning an infection in my feet...so can any one help me?
Ngole Reply
what sort of infection?
Dein-aboh
is the blood pressure increase? why?
Jumana Reply
hey
Chevelle
hello
lennox
how are you
Chevelle
I'm good
lennox
And how are you doing
lennox
ok
Chevelle
And how are you doing
lennox
are you single
Chevelle
is that scientific chat or what 😅
Mutaz
yes it is
Chevelle
more like a dating chat
Oliver
lool.. how?
Mutaz
ok
Chevelle
what is the reason for cardiac arrest
Oseni Reply
stop the heat suddenly
It's usually triggered when there's a malfunction in the heart which causes arrhythmia..hope u get more clarity online
Dein-aboh
what is cardiovascular system
Mohamed
y
cardiovascular system in a lame mans under
Dein-aboh
what y
Mohamed
the heart
Ashley
cardiovascular system is a system that circulates blood and lymph through the body, consisting of the heart, blood vessels, blood, lymph, and the lymphatic vessels and glands
Dein-aboh
thanks dein-aboh perfect
Mohamed
your welcome bro
Dein-aboh
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, An introduction to the fdm-tdm digital transmultiplexer. OpenStax CNX. Nov 16, 2010 Download for free at http://cnx.org/content/col11165/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'An introduction to the fdm-tdm digital transmultiplexer' conversation and receive update notifications?

Ask