# 0.4 The impact of digital tuning on the overall design of an fdm

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## Problem statement

So far we have presumed that the FDM input signal to the transmux has been magically provided and that it has been sampled at the proper rate. In fact, the signal available to the processor might not be in the desired form and signal processing may be required to convert it appropriately. As we shall see, the computation required for this can be significant in itself. As a result, these signal conditioning steps must be taken into account in the optimal design of the whole system. In this section, we focus on the use of digital tuners for this signal conditioning and examine the tradeoffs between the parameters of a tuner and the transmultiplexer that follows it.

## Total computational requirements

There are a few practical applications in which the input signal is complex-valued, sampled at the desired rate, and spectrally registered with the filters produced by the transmux-based filter bank. More typically, however, applications involve real-valued input signals, the signal is not aligned with the filters in the bank, or the signal of interest must be extracted from a wideband signal. It is common in these cases to use a digital tuner to select the portion of the spectral band in which the transmux will operate. This tuner will usually have a block diagram exactly like that seen in Figure 1 from "Derivation of the equations for a Basic FDM-TDM Transmux" . The incoming sampled signal is quadrature downconverted, filtered using an FIR linear phase filter, and then decimated We assume one-step decimation in this analysis. An important exception to this approach is described in Section 5.4.3. . The decimated tuner output is applied to the preprocessor portion of the transmultiplexer. For the analysis here we assume that the input is real-valued (from an A/D converter, for example), that the tuner input sampling rate is given by ${f}_{in}$ , that the pulse response duration of the tuner's filter is given by L t and that its decimation factor is M t . The spectral band over which the tuner offers rated passband performance and adjacent signal rejection is denoted by B t . The combined block diagram of the tuner and FDM-TDM transmultiplexer is shown in [link] , along with the key variables needed to determine the joint optimal design.

We obtain an equation for the total number of multiply-adds required by adding the transmux expression found in Equation 18 from "Derivation of the equations for a Basic FDM-TDM Transmux" with the computation requirements of the preceding tuner. This produces the following:

${G}_{\mathrm{total}}\phantom{\rule{4pt}{0ex}}=\phantom{\rule{4pt}{0ex}}{G}_{\mathrm{tuner}}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}{G}_{\mathrm{transmux}}$
$=2{f}_{in}\left\{1+\frac{{L}_{t}}{{M}_{t}}\right\}+\frac{2{f}_{s}N}{M}·\left\{Q+lo{g}_{2}N\right\}.$

By inspection we see that $\frac{fin}{{M}_{t}}={f}_{s}$ and that ${f}_{\mathrm{out}}=\frac{{f}_{s}}{M}=\frac{{f}_{in}}{{M}_{t}M}$ .

We observe that the bandwidth of the signal exiting the tuner, denoted B t , must be less than f s , the transmux input rate, in order to satisfy the Nyquist sampling theorem. Their ratio is a key element in the computational tradeoff between the tuner and the transmux. With B t fixed, an increase in f s increases the computation needed for the transmux while decreasing that needed for the tuner. We make this explicit by developing a formula for the tuner's pulse response duration L t . Again assuming one-step decimation and appealing to the design formulas discussed in [link] , L t is closely approximated by

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
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da
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Bhagvanji
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Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
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Alexandre
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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
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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?
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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
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