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user409495
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What is the variance of the convolution of two random variables?

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user409495
user409495
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Consider two random variables $Z$ and $w$$W$. Given the variances of $Z$ and $w$$W$, how can we compute the variance of their convolution $Z \circledast w $$Z \circledast W $?

As an example, please consider the case of noise ($Z$) in an image being modeled by a Gaussian distribution of zero mean and a given variance $\sigma_Z^2$. Suppose we perform a convolution of $Z$ with a Gaussian kernel denoted by $w$$W$. How can we find the variance of $Z \circledast w $$Z \circledast W $? I am not able to find a good reference for this. Thanks for any help.

Consider two random variables $Z$ and $w$. Given the variances of $Z$ and $w$, how can we compute the variance of their convolution $Z \circledast w $?

As an example, please consider the case of noise ($Z$) in an image being modeled by a Gaussian distribution of zero mean and a given variance $\sigma_Z^2$. Suppose we perform a convolution of $Z$ with a Gaussian kernel denoted by $w$. How can we find the variance of $Z \circledast w $? I am not able to find a good reference for this. Thanks for any help.

Consider two random variables $Z$ and $W$. Given the variances of $Z$ and $W$, how can we compute the variance of their convolution $Z \circledast W $?

As an example, please consider the case of noise ($Z$) in an image being modeled by a Gaussian distribution of zero mean and a given variance $\sigma_Z^2$. Suppose we perform a convolution of $Z$ with a Gaussian kernel denoted by $W$. How can we find the variance of $Z \circledast W $? I am not able to find a good reference for this. Thanks for any help.

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user409495
user409495
  • 1
  • 2

What is the variance of the convolution of two random variables?

Consider two random variables $Z$ and $w$. Given the variances of $Z$ and $w$, how can we compute the variance of their convolution $Z \circledast w $?

As an example, please consider the case of noise ($Z$) in an image being modeled by a Gaussian distribution of zero mean and a given variance $\sigma_Z^2$. Suppose we perform a convolution of $Z$ with a Gaussian kernel denoted by $w$. How can we find the variance of $Z \circledast w $? I am not able to find a good reference for this. Thanks for any help.