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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 0 . 38 for J N ( a ) is explicable because 0 . 38 2 0 . 15 = s 2 . The convergent value of a = 0 . 22 for J L S ( a ) 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 s 2 . Rather, J L S ( a ) calculates a smaller gain that makes avg { s 2 } 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 Equation 30 and Equation 34 each have two minima. As long as a can be initialized with the correct (positive) sign, there is little danger of converging to the wrong minimum.
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 L S ( a ) can be expressed as

± s 2 k r k 2 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 ( a ) = 1 2 a 2 ( 1 2 s 2 [ k ] 3 - s 2 ) . 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 ( a ) 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 ( a ) and J L S ( a ) .

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] .

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
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I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
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Commplementary angles
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what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
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rolling four fair dice and getting an even number an all four dice
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Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
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linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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Ramkumar Reply
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Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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