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Calculation of expected value in terms ACF

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How to find expexted value of system output in terms of transfer function with knowing expected value of input and autocorrelation function of input?

I should find Expectation of $y(t)=int x(t-tau)h(tau ,t)dtau $ in terms of transfer function.
I have started with : $y(t)=int H(f,t)x(f)e^jpi ft)df$

But I have no idea what I can do with that...

statistics random correlation expected-value

share|cite|improve this question

edited Mar 14 at 7:49

Nani

asked Mar 8 at 8:27

NaniNani

32

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  I don't think the ACF will uniquely determine the expected value. If $y_t = c + x_t$ where $c$ is a constant, then $x_t$ and $y_t$ have same autocorrelation functions but different means (since adding a constant doesn't affect correlation).
  $endgroup$
  – Minus One-Twelfth
  Mar 14 at 7:26
  
  

  
  
  
  


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  @MinusOne-Twelfth i didnt find any formulas. In task ACF and expectation of x(t) are given and i need to calculate the expectation of y(t)....So i think that ACF and Expectation should have a relation...
  $endgroup$
  – Nani
  Mar 14 at 7:51
  

  
  
  
  


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  Ah sorry, I thought you didn't know the expected value of the input series.
  $endgroup$
  – Minus One-Twelfth
  Mar 14 at 7:54
  

  
  
  
  

add a comment | 

0

$begingroup$

How to find expexted value of system output in terms of transfer function with knowing expected value of input and autocorrelation function of input?

I should find Expectation of $y(t)=int x(t-tau)h(tau ,t)dtau $ in terms of transfer function.
I have started with : $y(t)=int H(f,t)x(f)e^jpi ft)df$

But I have no idea what I can do with that...

statistics random correlation expected-value

share|cite|improve this question

edited Mar 14 at 7:49

Nani

asked Mar 8 at 8:27

NaniNani

32

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't think the ACF will uniquely determine the expected value. If $y_t = c + x_t$ where $c$ is a constant, then $x_t$ and $y_t$ have same autocorrelation functions but different means (since adding a constant doesn't affect correlation).
  $endgroup$
  – Minus One-Twelfth
  Mar 14 at 7:26
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @MinusOne-Twelfth i didnt find any formulas. In task ACF and expectation of x(t) are given and i need to calculate the expectation of y(t)....So i think that ACF and Expectation should have a relation...
  $endgroup$
  – Nani
  Mar 14 at 7:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ah sorry, I thought you didn't know the expected value of the input series.
  $endgroup$
  – Minus One-Twelfth
  Mar 14 at 7:54
  

  
  
  
  

add a comment | 

$begingroup$

How to find expexted value of system output in terms of transfer function with knowing expected value of input and autocorrelation function of input?

I should find Expectation of $y(t)=int x(t-tau)h(tau ,t)dtau $ in terms of transfer function.
I have started with : $y(t)=int H(f,t)x(f)e^jpi ft)df$

But I have no idea what I can do with that...

statistics random correlation expected-value

share|cite|improve this question

edited Mar 14 at 7:49

Nani

asked Mar 8 at 8:27

NaniNani

32

$endgroup$

share|cite|improve this question

edited Mar 14 at 7:49

Nani

asked Mar 8 at 8:27

NaniNani

32

share|cite|improve this question

edited Mar 14 at 7:49

Nani

asked Mar 8 at 8:27

NaniNani

32

asked Mar 8 at 8:27

NaniNani

32

asked Mar 8 at 8:27

NaniNani

32