Posted by
Michael Schmid on
Nov 11, 2014; 11:10am
URL: http://imagej.273.s1.nabble.com/Convolution-of-Arrays-tp5010371p5010372.html
Hi Greg,
hmm, having the full FFT/FD math functionality for 1D arrays would be quite a bit of work.
Why not do the convolution without the FFT, point by point?
http://en.wikipedia.org/wiki/Convolution#Discrete_convolutionTypically, 1D arrays don't have millions of points, so the computing time is not as much an issue as for 2D images.
Also, when doing it directly without FFT, you have more choices for how to treat the boundaries; having periodic repetition or not, dividing by the length of the overlap in case of no periodic boundary conditions, using windowing functions for the overlap area, etc. If desired, you can easily have periodic boundary conditions with an array length that is not a power of 2. Just a lot of flexibility that you will never get from the FFT approach.
Michael
________________________________________________________________
On Nov 11, 2014, at 11:59, Gregory James wrote:
> Dear ImageJ community,
>
> I would like to convolve two functions together. My data are in two 1-D arrays. I was very excited with the recent introduction of the 'Array.fourier' function. Thank you to the ImageJ administrators for this.
>
> The problem I'm having is that I can perform the multiplication in Fourier space to do the convolution but then I can not transform the result back into real space. Are there any plans to introduce an inverse function to 'Array.fourier'?
>
> I've also tried representing my 1-D arrays as images then using the FFT functionality, but this doesn't seem to be working.
>
> Does anyone have any bright ideas as to how I can convolve two functions together?
>
> Thank you very much,
>
> Greg.
>
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