Questions tagged [convolution]

Tags for questions about convolution, including the Mathematica functions Convolve, DiscreteConvolve, ListConvolve, DirichletConvolve, ImageConvolve, and convolutions using Fourier, FourierTransform, or LaplaceTransform.

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28
votes
3answers
4k views

How to find the center of a circular pattern?

I am writing an algorithm that finds the center of 500 x 500 pixels images coming from a live feed from a camera at 50 Hz. So it has to be quick! The images are images of an optical field which looks ...
9
votes
3answers
4k views

Discrete Convolution

Ask to compute the convolution of 2 lists, I managed to do so, with what I feel is rather heavy : Let my 2 lists be : a = {1,2,3,4} b = {1,1,1,1,1,1}; The below function adds 0s on each part of ...
5
votes
1answer
1k views

Challenge: deblurring images [duplicate]

My friend came back from holidays, where he took lots of pictures. Unfortunately, the camera was set on manual focus and most pictures are blurry. It got me thinking that mathematica showed how to ...
10
votes
4answers
4k views

cross-correlation with time lag

I have two lists with some data. a={1,2,3,4,5} b={5,4,3,2,1} Now I want to compute the cross correlation of the two lists with a time lag of 1, like it is ...
2
votes
0answers
351 views

How can estimate the PSF function to deblur an image of plate licence of a car [duplicate]

I want to deblur an image of a licence plate of a car. I have used the ImageDeconvolve[] function and Sharpen[] but the problem ...
1
vote
2answers
134 views

Getting Convolve to behave in preparation for NonlinearModelFit

New information added at bottom of post This is an outgrowth of this earlier question. Let us suppose that we have an instrumental response function given here: ...
7
votes
2answers
723 views

Does Mathematica reuse previous computations?

I am doing an analysis of experimental results in which I need to repeat the same GaussianFilter hundred of times on different data. As explained in the ...
1
vote
0answers
130 views

How to solve ode with convolution?

my question is as this and i want to get the solution of this ode x(t) $ ({M_{33}}{\rm{ + }}{{\rm{m}}_{33}})x''(t) + \int\limits_{ - \infty }^t {x'(tau){K_{33}}(t -...
6
votes
1answer
2k views

Convolving/integrating problems

Let's say I want to convolve two functions (f and g), a gaussian with a breit-wigner: ...
4
votes
1answer
1k views

Convolve two sets of (x,y) data sets

I have two sets of data in the form a={{.1,2},{.2,3},{.3,4},{.5,6}} b={{0,8},{.1,4},{.2,7},{.3,1},{.5,10},{.6,3}} Both data sets have even spacing, although ...
2
votes
1answer
166 views

Rewrite the power sum in terms of convolution

Let be an identity $$n^{2m+1}=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1}k^r(n-k)^r,$$ where $A_{m,r}$ are real coefficients, see A302971 for numerators and formula of $A_{m,r}$. Here we can notice that $\...
0
votes
1answer
85 views

Convolve gives inconsistent results if performed symbolically and numerically

Response from Wolfram Technical Support at end. Suppose that I have an instrument response function of the form: ...