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1answer
43 views

Discrete fourier transform and convolution — scaling factor?

I am trying to convolve a square wave (a diffraction grating phgrating with slits size \[CapitalLambda]) with a point spread ...
1
vote
1answer
101 views

Convolution in Fourier domain

I am computing the convolution of a disk Img in 2D numerical matrix form with a kernel Ker in the Fourier domain but the output ...
0
votes
0answers
47 views

Discrete convolution power

In my previous question we have discussed the posibility of various definition of convolution of power function within Mathematica. Now the question is "How to define convolution power in Mathematica ?...
3
votes
0answers
192 views

Deconvolution using Fourier transforms

I have a 2D signal in the form of a function $g(x_m,y_m)$ given as $$ \begin{aligned} g(x_m,y_m) = \ & \int^{\infty}_{-\infty} \mathrm{d}x_o \ \mathrm{d}y_o \ \frac{1}{\varepsilon^2} P(x_o - x_m,...
2
votes
0answers
72 views

Use List convolve for aligning images

I am trying to align images of point spread functions using a convolution. Before doing it on real data, I wanted to try on simulated data. I have no problem with the 1-D case where I create 2 ...
1
vote
1answer
142 views

normalization of convolution product when using Fourier transform

I'm trying to calculate the convolution of two probability density functions (PDFs) defined on the real axis: a normal distribution (with \[Sigma] > 0 and ...
6
votes
1answer
260 views

single slit diffraction numerical simulation

I'm trying to simulate the Fraunhoffer diffraction at slits(single,double,triple) with Mathematica. In the picture, the red one is analytical result and the green one is numerical result. The ...
0
votes
1answer
138 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
3
votes
0answers
198 views

Analytical Fourier Transforms with convolution rule [closed]

The task is the following, how to extend Mathematica's FourierTransform command in order to be able to analytically deal with non-linear differential equations. To do so it should be able to deal with ...
1
vote
0answers
588 views

Mathematica does not calculate inverse fourier transformation or the convolution of two functions

I am trying to take convolution of a Gaussian function with an exponential function. Mathematica couldn't calculate it. ...
4
votes
1answer
2k views

How do you use Fourier transforms to perform a deconvolution

I've been trying to teach myself about deconvolution through Fourier transforms, but I seem to be missing something simple, as my results are garbage. I start by defining a test function and a window ...