Find the mean and autocorrelation
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I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
$phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
frac4pi, quad |varphi | leq fracpi8
\
0, quad mathrmotherwise.
endmatrixright.$
Find the mean and autocorrelation functions.
- Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?
statistics stationary-processes
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up vote
1
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favorite
I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
$phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
frac4pi, quad |varphi | leq fracpi8
\
0, quad mathrmotherwise.
endmatrixright.$
Find the mean and autocorrelation functions.
- Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?
statistics stationary-processes
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
$phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
frac4pi, quad |varphi | leq fracpi8
\
0, quad mathrmotherwise.
endmatrixright.$
Find the mean and autocorrelation functions.
- Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?
statistics stationary-processes
I have this problem. Consider a random process X(t) defined by $X(t) = 2cos(2 pi t+ phi)$.
$phi$ is a random variable with probability density function $f_phi (varphi ) = left{beginmatrix
frac4pi, quad |varphi | leq fracpi8
\
0, quad mathrmotherwise.
endmatrixright.$
Find the mean and autocorrelation functions.
- Normally when I have a problem like this, the information about the values for which the phase is changing randomly, e.g., from $-pi$ to $pi$. And then i use the formula (the random process is $cos(..)$ in this example) $int_-pi^pi cos(...) frac12 pi dx$ and afterward i calculate the autocorrelation by calculating $E[cos(t_1...)cos(t_2dots)]$. In this problem, the density function is given instead. I know that i should check for if the mean is constant for all $t$. Can I say the mean is $frac12 pi$ for all $t$? And if that is correct, how should I calculate the autocrorrealtion?
statistics stationary-processes
edited Aug 21 at 12:34
Davide Giraudo
121k15147250
121k15147250
asked Dec 28 '17 at 16:24
Xraycat922
154
154
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