Convolution of a gaussian function and a hole

[Newser]

Hello,

I want to do the convolution of a gaussian function and a hole. If I want to use Fourier transform which functions should I use? Can I use rms? I want to calculate the spot size of a gaussian signal after a circular aperture.

Thanks!

 

[DrRocket]

Hello,

I want to do the convolution of a gaussian function and a hole. If I want to use Fourier transform which functions should I use? Can I use rms? I want to calculate the spot size of a gaussian signal after a circular aperture.

Thanks!

rms has nothing to do with either convolutions or Fourier transforms. Use the Fourier transform for whatever function you mean by a "hole". Fourier transform of a Gaussian is also a Gaussian.

 

[Newser]

Thanks for the reply. Yes, I know rms has nothing to do with Fourier transform, I was asking if I could use it instead...

 

[DrRocket]

Thanks for the reply. Yes, I know rms has nothing to do with Fourier transform, I was asking if I could use it instead...

Instead of what ?

It has nothing to do with the Fourier transform. It has nothing to do with convolution.

You question involved convolution.

Do you understand what convolution is ? And do you understand the relationship between the convolution algebra L^1(\mathbb R^n) and the algebra C_0( \mathbb R^n) ?

Both are Banach algebras and the Fourier transform is a continuous homomorphism from L^1(\mathbb R^n) to C_0( \mathbb R^n) which is injective but not surjective. Thus the Fourier transform can sometimes be used to calculate convolutions that are difficult to calculate directly. It takes convolutions (hard to understand) to pointwise multiplication (easy to understand).

 

[Newser]

Yes, I do understand what a convolution is, I think you are the one not understanding my question. I am not asking how to calculate a convolution, obviously if I am talking about Fourier transform I know how to do this...I was wondering about the most suited way to model this physical phenomenon (beam after aperture). But I guess I shouldn't have posted in this section of the forum, I thought I would found multi-skilled people...