# 0.5 Sampling with automatic gain control  (Page 18/19)

 Page 18 / 19

But why do the two algorithms converge to different places? The facile answer is that they are different becausethey minimize different performance functions. Indeed, the error surfaces in [link] show minima in different locations. The convergent value of $a\approx 0.38$ for ${J}_{N}\left(a\right)$ is explicable because $0.{38}^{2}\approx 0.15={\mathbf{s}}^{2}$ . The convergent value of $a=0.22$ for ${J}_{LS}\left(a\right)$ is calculated in closed form in Exercise  [link] , and this value does a good job minimizing its cost,but it has not solved the problem of making ${a}^{2}$ close to ${\mathbf{s}}^{2}$ . Rather, ${J}_{LS}\left(a\right)$ calculates a smaller gain that makes $\text{avg}\left\{{s}^{2}\right\}\approx {\mathbf{s}}^{2}$ . The minima are different. The moral is this:Be wary of your performance functions—they may do what you ask.

Use agcgrad.m to investigate the AGC algorithm.

1. What range of stepsize mu works? Can the stepsize be too small?Can the stepsize be too large?
2. How does the stepsize mu effect the convergence rate?
3. How does the variance of the input effect the convergent value of a ?
4. What range of averages lenavg works? Can lenavg be too small? Can lenavg be too large?
5. How does lenavg effect the convergence rate?

Show that the value of $a$ that achieves the minimum of ${J}_{LS}\left(a\right)$ can be expressed as

$±\sqrt{\frac{{\mathbf{s}}^{2}{\sum }_{k}{r}_{k}^{2}}{{\sum }_{k}{r}_{k}^{4}}}.$

Is there a way to use this (closed form) solution to replace the iteration [link] ?

Consider the alternative objective function $J\left(a\right)=\frac{1}{2}{a}^{2}\left(\frac{1}{2}\frac{{s}^{2}\left[k\right]}{3}-{\mathbf{s}}^{2}\right)$ . Calculate the derivative and implement avariation of the AGC algorithm that minimizes this objective. How does this version compare to the algorithms [link] and [link] ? Draw the error surface for this algorithm. Which version is preferable?

Try initializing the estimate a(1)=-2 in agcgrad.m . Which minimum does the algorithm find? What happens tothe data record?

Create your own objective function $J\left(a\right)$ for the AGC problem. Calculate the derivative and implement avariation of the AGC algorithm that minimizes this objective. How does this version compare to the algorithms [link] and [link] ? Draw the error surface for your algorithm. Which version do you prefer?

Investigate how the error surface depends on the input signal. Replace randn with rand in agcerrorsurf.m and draw the error surfaces for both ${J}_{N}\left(a\right)$ and ${J}_{LS}\left(a\right)$ .

## Using an agc to combat fading

One of the impairments encountered in transmission systems is the degradation due to fading, when the strengthof the received signal changes in response to changes in the transmission path. (Recall the discussion in [link] .) This section shows how an AGC can be used to counteractthe fading, assuming the rate of the fading is slow, and provided the signal does not disappear completely.

Suppose that the input consists of a random sequence undulating slowly up and down in magnitude, as in the topplot of [link] . The adaptive AGC compensates for the amplitude variations,growing small when the power of the input is large, and large when the power of the input is small. This is shown in themiddle graph. The resulting output is of roughly constant amplitude, as shown in the bottom plot of [link] .

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
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
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