# 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. Key Variables in the Size Optimization of a Digital Tuner and Transmultiplexer

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

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
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
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
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 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! By    By   By David Martin  By Rhodes