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January 28th, 2009, 08:45 AM   #1
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Convolution of two Gaussian Functions

Hi,
i have to convolve this two functions


i now the solution, it's:

so i've no idea which steps i have to go to get this solution,
hope anybody can help me
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January 28th, 2009, 04:52 PM   #2
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Re: Convolution of two Gaussian Functions

Quote:
Originally Posted by scratch
Hi,
i have to convolve this two functions


i now the solution, it's:

so i've no idea which steps i have to go to get this solution,
hope anybody can help me
There are two ways.

The most direct way is write down the convolution integrand and play around with the exponent.

An indirect, but simpler way, is to take the Fourier transforms, which is very easy for these functions. The transforms will look very similar to the functions themselves. Then multiply the transforms together and take the back transform.
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January 29th, 2009, 05:22 AM   #3
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Re: Convolution of two Gaussian Functions

thank u very much, i got it
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October 9th, 2015, 04:29 AM   #4
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If your Gaussians are univariate, a whole solution is available here:
http://www.tina-vision.net/docs/memos/2003-003.pdf
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October 13th, 2015, 08:13 AM   #5
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This is equivalent to the statement that if X1 and X2 are normally distributed with mean zero and variances s1^2 and s2^2, then their sum is normally distributed with zero mean and variance s1^2 + s2^2
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