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

 Page 1 / 7

## 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

#### Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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?
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
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!