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Asked: 2026-05-27T10:08:26+00:00

I have a two vectors of spatial data (each about 2000 elements in length).

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I have a two vectors of spatial data (each about 2000 elements in length). One is a convolved version of the other. I am trying to determine the kernel that would produce such a convolution. I know that I can do this by finding the inverse Fourier transform of the ratio of the Fourier transforms of the output and input vectors. Indeed, when I do this I get more or less the shape I was expecting. However, my kernel vector has the same dimensionality as the two input vectors when in reality the convolution was only using about one fifth (~300-400) of the points. The fact that I am getting the right shape but the wrong number of points makes me think that I am not using the ifft and fft functions quite correctly. It seems like if I were really doing the right thing this should happen naturally. At the moment I am simply doing;

FTInput = fft(in);
FtOutput = fft(out);
kernel = ifft(FtOutput./FTInput).

Is this correct and it’s up to me to interpret the output vector correctly or have I oversimplified the task? I’m sure it’s the latter, I’m just not sure where.

Thanks

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1 Answer

  1. Editorial Team

    You are doing things correctly, this is not a bug.

    The problem of estimating a convolution filter given clean and convolved data is VERY HARD. Given “nice” data, you may get the right shape but retrieving the true support of the convolution filter (i.e. getting zeroes where they should be) is NOT going to happen naturally.

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