Study the autocorrelation function

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  • #26
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You should follow the approach in this post: https://www.physicsforums.com/showthread.php?p=1387935#post1387935[/QUOTE]

Thank you very much for being patient with me!!
Do you know what my exact problem is?
I am going to transmit a signal, which it is described by Hn(t).
I want to prove the orthogonality of this function by using different derivative for this signal, If they are orthogonal to each other or not.
So, I suggest to find the autocorrelation function for them, I mean between H1(t) and H2(t). After that I have to find the mean and the variance for the result of autocorrelation function.

Am I on the correct way?
 
  • #27
EnumaElish
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I am not sure I understand completely. Can you fill in the blanks in the following statement:

"I'd like to show function ___ is orthogonal to function ___."

If your answers are H1 and H2, then why does this have anything to do with the AC function? In this case, you need to prove Cov(H1,H2) = 0, which is different than the AC function.

On the other hand, if your statement is "I'd like to show function H[n] is orthogonal with itself (over time)" (i.e. AC=0), then you are correct to study the AC function.
 
  • #28
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I am not sure I understand completely. Can you fill in the blanks in the following statement:

"I'd like to show function _H1_ is orthogonal to function _H2_."

If your answers are H1 and H2, then why does this have anything to do with the AC function? In this case, you need to prove Cov(H1,H2) = 0, which is different than the AC function.

On the other hand, if your statement is "I'd like to show function H[n] is orthogonal with itself (over time)" (i.e. AC=0), then you are correct to study the AC function.
"I'd like to show function _H1_ is orthogonal to function _H2_."
 
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  • #29
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when we want to receive these signals, a correlation receiver will be used
So, the autocorrelation function for the transmitted signal should be determined and from the result of the autocorrelation function we will determine the Mean and Variance
 
  • #30
EnumaElish
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"I'd like to show function _H1_ is orthogonal to function _H2_."
The way to show H1 is orthogonal to H2 is to show Cov(H1,H2) = 0. This does not have anything with the AC function, which is a very specific transformation of a single parent function (for example, H1) with itself, over time (over a very short time interval).
So, the autocorrelation function for the transmitted signal should be determined and from the result of the autocorrelation function we will determine the Mean and Variance
I am not a signal processing engineer. I don't know what a correlation receiver is.

My best understanding is this:
You are trying to find the autocorrelation coefficient of a signal. http://en.wikipedia.org/wiki/Autocorrelation#Signal_processing

You need to first determine the Rff(T) function.

Then you'd like to convert it into an AC coefficient as: r(T) = [Rff(T) - Meanf(T)^2]/Varf(T). http://en.wikipedia.org/wiki/Autocovariance (look under "Normalization")

Am I close?

You can determine Rff(T) analytically. But a simpler method is computer simulation. If you simulate N signals from your H1 function, then you can calculate the autocorrelation coefficient numerically (for n lags, or t - n), as in this link: http://w3eos.whoi.edu/12.747/notes/lect06/l06s02.html
 
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  • #31
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My best understanding is this:
You are trying to find the autocorrelation coefficient of a signal. http://en.wikipedia.org/wiki/Autocorrelation#Signal_processing

You need to first determine the Rff(T) function.

Then you'd like to convert it into an AC coefficient as: r(T) = [Rff(T) - Meanf(T)^2]/Varf(T). http://en.wikipedia.org/wiki/Autocovariance (look under "Normalization")

Am I close?
yes, exactly! My points are to determine the mean and variance.
So, as I understand from your comments that if I will find the correlation coefficient then I can determine the mean and variance.
 
  • #32
EnumaElish
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No. Typically you need to:
1. Calculate the mean
2. Calculate the variance
3. Calculate Rff
4. Put 1, 2, 3 together to calculate r (the corr. coeff.).

Is this helpful? If not, why not?
 
  • #33
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No. Typically you need to:
1. Calculate the mean
2. Calculate the variance
3. Calculate Rff
4. Put 1, 2, 3 together to calculate r (the corr. coeff.).

Is this helpful? If not, why not?
Yes, it’s fine. I agree.
But I think I should start with determining Rff(T) and after that the mean and variance.
Is that’s right?
 
  • #34
EnumaElish
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Any order would be fine.
 

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