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

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## Relationship of the filter bank approach to digital spectrum analysis

A matter of confusion to many engineers is that the filter bank scheme seems to produce time samples from FFT bins. This confusion has its root in the fact that the DFT, and hence the FFT, are usually discussed in the context of digital spectrum analysis and are typically spoken of as methods of converting from the time domain to the frequency domain. How then can a DFT-based filter bank produce time samples from spectral bins? In fact, the right perspective is the opposite one.

Consider again [link] from the viewpoint of digital spectrum analysis. A simple FFT-based spectrum analyzer accepts N samples of the input sequence, weights or windows the data, transforms it by using an N-point FFT, and then estimates the power spectral density by computing the magnitude square of the bin outputs. Comparing these steps to [link] , we see that they are identical except for two things: (1) the magnitude squaring operation at the bin outputs and (2) the fact that in spectrum analysis the window and transform operation is rarely done for every input sample. (Typically it is done every N-th sample [called 1:1 overlapping ] or even less frequently.) These facts suggest that DFT/FFT-based digital spectrum analysis is derived from the filter bank concept rather than the other way around. The filter bank shown in [link] uses a transform computed over a record of weighted, delayed input data to split the input signal's energy into N spectral bands. The degree to which this separation is completed depends on the choice of windowing or weighting function and on the length of the transform. If the function is chosen properly, the windowing operation and the DFT/FFT computation can be computed less frequently, that is, decimation can be introduced. In this context, the simple FFT-based spectrum analyzer can be recognized to perform an instantaneous power measurement at the output of each of the filters in the bank. The quality of the analyzer depends on the window function chosen and the DFT/FFT order N (as they affect the passband shape), the rate at which the filter outputs are computed (given by the decimation factor M ), and the number of instantaneous power measurements averaged to obtain the spectral estimate. Thus we can conclude that the digital spectrum analyzer approximates the true power spectrum by measuring the power seen in each of the bandpass filter outputs produced by the DFT-based filter bank.

An interesting sidelight is that the most common name for the transmultiplexer preprocessor stems from the filter bank's relationship with digital spectrum analysis. Look again at [link] . The input to the QN-point FFT is $QN$ weighted and delayed input samples. From the bank-of-tuners viewpoint we know that the weighting function $w\left(k\right)$ is just the tuner pulse response $h\left(k\right)$ needed to bandlimit the tuned signal properly. In the context of spectrum analysis, however, this function is called a data window. They are in fact identical and the tuner viewpoint provides the analytical basis on which to design the needed window. We've already observed that after pruning the FFT, the QN-point transform separates into two sections. The first section folds together Q windowed samples at a time to generate the N-point input to the FFT. From this viewpoint, it is commonly referred to as the window-and-fold section of the FDM-to-TDM transmultiplexer.

## Stylized fortran implementation of a basic fdm-tdm transmux

Table 1 shows a stylized example of a software implementation of an FDM-TDM transmultiplexer. Some details of the initialization steps have been blurred for the sake of simplicity and the parameters user are certainly not those appropriate to all applications, but the code should serve as an accurate guide to the amount of computation needed and its organization.

SUBROUTINE TMUX(INPUT_ARRAY, INPUT_POINTER, OUTPUT_VECTOR) CC SUBROUTINE TMUX - IMPLEMENTS A BASIC FDM-TO-TDM TRANSMUX. C A NEW VECTOR OF CHANNELIZED CHANNEL OUTPUTS, CALLEDC "OUTPUT_VECTOR" IS PRODUCED EACH TIME THE SUBROUTINE IS CALLED, C UNLESS THE DATA IN "INPUT_ARRAY" IS EXPENDED.C PARAMETER N = 64 !NUMBER OF CHANNELS AND/OR BINSPARAMETER Q = 3 !WEIGHTING FUNCTION EXPANSION FACTOR PARAMETER M = N !DECIMATION FACTORC THIS CHOICE OF M YIELDS BASIC TRANSMUX CINTEGER M, N, Q, INPUT_POINTER, J, K, INDEX COMPLEX INPUT_ARRAY(1), OUTPUT_VECTORS(N), VRP(N)REAL WEIGHTING(N*Q) CDATA WEIGHTING/ * QN values of the weighting function h(k) */ CC ****************** MOVE TIME POINTER ************************** CINPUT_POINTER = INPUT_POINTER + M CC ****************** COMPUTE v(r,p) ***************************** CDO 10 J=1,N 10 VRP(J) = CMPLX(0.,0.) !ZERO THE VECTOR VRPC DO 30 J=1,NDO 20 K=1 Q INDEX = (K-1)*N+J-1 !COMPUTE OFFSET IN DATA AND WEIGHTINGVRP(J) = VRP(J) + INPUT_ARRAY(INPUT_POINTER -INDEX) * 1 WEIGHTING(INDEX+1)20 CONTINUE 30 CONTINUEC C ****************** COMPUTE VECTOR OF OUTPUTS ******************C ****************** USING INVERSE FFT ROUTINE ****************** CCALL IFFT(VRP,OUTPUT_VECTOR,N) CC ****************** REMOVE RESIDUAL CARRIER TERM *************** CC ------------ IF M NOT EQUAL TO N, REMOVE CARRIER HERE CC ********************* NORMAL RETURN *************************** CRETURN CEND Stylized FORTRAN Example of an FDM-TDM Transmultiplexer 

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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