http://imagej.273.s1.nabble.com/Convolution-of-Arrays-tp5010371p5010522.html
Just a note, also the FFT Convolution supports any outofbounds strategy … the image is simply extended by half the kernel size using the desired outofboundsstrategy before computing the FFT based convolution.
> On Nov 17, 2014, at 18:12 , Curtis Rueden <
[hidden email]> wrote:
>
> Hi Greg,
>
>> Does anyone have any bright ideas as to how I can convolve two
>> functions together?
>
> You might also find the ImgLib2 library useful. See the ImgLib2 Tutorials
> for relevant examples.
>
>
http://imagej.net/ImgLib2_Examples>
http://imagej.net/ImgLib2_Examples#Example_6b_-_Convolution_in_Fourier_space>
> Regards,
> Curtis
>
> On Tue, Nov 11, 2014 at 5:10 AM, Michael Schmid <
[hidden email]>
> wrote:
>
>> 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_convolution>>
>> Typically, 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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