My Math Forum Convolution of two Gaussian Functions
 User Name Remember Me? Password

 Real Analysis Real Analysis Math Forum

 January 28th, 2009, 08:45 AM #1 Newbie   Joined: Jan 2009 Posts: 2 Thanks: 0 Convolution of two Gaussian Functions Hi, i have to convolve this two functions $g(x)=e^{-\pi(\frac{x}{a})^2}$ $h(x)=e^{-\pi(\frac{x}{b})^2}$ i now the solution, it's: $\frac{a\cdot b}{\sqrt{a^2+b^2}}\cdot e^{-\frac{\pi u^2}{a^2+b^2}$ so i've no idea which steps i have to go to get this solution, hope anybody can help me
January 28th, 2009, 04:52 PM   #2
Global Moderator

Joined: May 2007

Posts: 6,398
Thanks: 546

Re: Convolution of two Gaussian Functions

Quote:
 Originally Posted by scratch Hi, i have to convolve this two functions $g(x)=e^{-\pi(\frac{x}{a})^2}$ $h(x)=e^{-\pi(\frac{x}{b})^2}$ i now the solution, it's: $\frac{a\cdot b}{\sqrt{a^2+b^2}}\cdot e^{-\frac{\pi u^2}{a^2+b^2}$ 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.

 January 29th, 2009, 05:22 AM #3 Newbie   Joined: Jan 2009 Posts: 2 Thanks: 0 Re: Convolution of two Gaussian Functions thank u very much, i got it
 October 9th, 2015, 04:29 AM #4 Newbie   Joined: Oct 2015 From: Austria Posts: 2 Thanks: 0 If your Gaussians are univariate, a whole solution is available here: http://www.tina-vision.net/docs/memos/2003-003.pdf
 October 13th, 2015, 08:13 AM #5 Newbie   Joined: Sep 2015 From: New york Posts: 17 Thanks: 4 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

 Tags convolution, functions, gaussian

Search tags for this page

,

### convolution of two gaussians

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post muzialis Calculus 0 June 2nd, 2012 02:20 AM token22 Real Analysis 8 May 24th, 2011 03:07 PM everk Real Analysis 1 November 25th, 2010 02:12 PM germanaries Complex Analysis 0 January 15th, 2008 12:38 PM vuudu Real Analysis 0 November 3rd, 2007 11:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2017 My Math Forum. All rights reserved.