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

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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. The error surface for the AGC objective functions [link] and [link] each have two minima. As long as a can be initialized with the correct (positive) sign, there is little danger of converging to the wrongminimum.

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] .

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
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
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
has a lot of application modern world
Kamaluddeen
yes
narayan
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
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
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