how to use correlation function main definition?
$begingroup$
I'm enrolled in a course off control where the formula for correlation was presented to us without any context .
$RX(t1,t2) = intint x1x2 fX(t1)X(t2)(x1,x2)dx1dx2$
the problema than I'm facing is then when we calculate for instances the correlation of X(t)=Acos(wt+a) ,where a is a uniform random variable in the interval [0,2$pi$] we do the following :
$RX(t1,t2) = frac{1}{2pi}int_{0}^{2pi}cos(wt1 + a)cos(wt2+a)da$
what happened to the double integral,and why is there only the integral in a and not two in a1 and a2 ? I apologize for the trivial question but has it is probably to obvious for someone who knows the meaning of the elements of the formula I couldn't find an explanation in the internet.
correlation
asked Jan 14 at 10:55
ricostynharicostynha
64
$endgroup$
add a comment |
$begingroup$
I'm enrolled in a course off control where the formula for correlation was presented to us without any context .
$RX(t1,t2) = intint x1x2 fX(t1)X(t2)(x1,x2)dx1dx2$
the problema than I'm facing is then when we calculate for instances the correlation of X(t)=Acos(wt+a) ,where a is a uniform random variable in the interval [0,2$pi$] we do the following :
$RX(t1,t2) = frac{1}{2pi}int_{0}^{2pi}cos(wt1 + a)cos(wt2+a)da$
what happened to the double integral,and why is there only the integral in a and not two in a1 and a2 ? I apologize for the trivial question but has it is probably to obvious for someone who knows the meaning of the elements of the formula I couldn't find an explanation in the internet.
correlation
asked Jan 14 at 10:55
ricostynharicostynha
64
$endgroup$
add a comment |
$begingroup$
I'm enrolled in a course off control where the formula for correlation was presented to us without any context .
$RX(t1,t2) = intint x1x2 fX(t1)X(t2)(x1,x2)dx1dx2$
the problema than I'm facing is then when we calculate for instances the correlation of X(t)=Acos(wt+a) ,where a is a uniform random variable in the interval [0,2$pi$] we do the following :
$RX(t1,t2) = frac{1}{2pi}int_{0}^{2pi}cos(wt1 + a)cos(wt2+a)da$
what happened to the double integral,and why is there only the integral in a and not two in a1 and a2 ? I apologize for the trivial question but has it is probably to obvious for someone who knows the meaning of the elements of the formula I couldn't find an explanation in the internet.
correlation
asked Jan 14 at 10:55
ricostynharicostynha
64
$endgroup$
I'm enrolled in a course off control where the formula for correlation was presented to us without any context .
$RX(t1,t2) = intint x1x2 fX(t1)X(t2)(x1,x2)dx1dx2$
the problema than I'm facing is then when we calculate for instances the correlation of X(t)=Acos(wt+a) ,where a is a uniform random variable in the interval [0,2$pi$] we do the following :
$RX(t1,t2) = frac{1}{2pi}int_{0}^{2pi}cos(wt1 + a)cos(wt2+a)da$
what happened to the double integral,and why is there only the integral in a and not two in a1 and a2 ? I apologize for the trivial question but has it is probably to obvious for someone who knows the meaning of the elements of the formula I couldn't find an explanation in the internet.
correlation
correlation
asked Jan 14 at 10:55
ricostynharicostynha
64
asked Jan 14 at 10:55
ricostynharicostynha
64
edited Jan 14 at 11:57
ricostynha
asked Jan 14 at 10:55
ricostynharicostynha
64
asked Jan 14 at 10:55
ricostynharicostynha
64
asked Jan 14 at 10:55
ricostynharicostynha
64
64
add a comment |
add a comment |
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