# How to convolve a 3D matrix along one of its dimension?

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Yuxin Tong on 26 Apr 2022
Commented: Yuxin Tong on 27 Apr 2022
I have a 100by100by2000 ish matrix, say 3rd dimention is representing time where the 100*100 matrix changes. I wanted to convolve this whole matrix through a temporal gaussian filter along the 3rd dimention (the one that is 2000ish long).
With the code I know of I can only think of making a for-loop and do conv() 10000 times. (cuz I believe conv() can only operat on single dimention vectors?) However this for-loop will then be extremely long and it seems like it would take forever to run. I have attached a visual illustration of what I wanted to do.
So my question is: is there a function that is equivilent to conv() that can allow me to do this in more eifficient way? Or can I actually make conv() to run in a vectorized way?
I am aware that there is a fucntion called filter(), but I wasnt really sure what does that function do. If filter actually would work can anyone tell me what is the similarity and difference between filter and conv?
Thx a lot. Matt J on 26 Apr 2022
If your Gaussian kernels is 1x1xN, you can just use convn as usual
kernel=reshape(gaussianProfile,1,1,[]);
output=convn(Array, kernel);
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Yuxin Tong on 27 Apr 2022
Thx! I think this worked!

### More Answers (3)

Akira Agata on 26 Apr 2022
The function smoothdata must be applicable, like:
% Sample data
A = rand(100, 100, 2000);
% Gaussian filter window
win = 15;
% Apply smoothdata along 3rd dimension
dim = 3;
A2 = smoothdata(A, dim, 'gaussian', win);
% Let's check!
figure
plot(squeeze(A(1, 1, :)),'c')
hold on
plot(squeeze(A2(1, 1, :)),'b')
legend({'Original', 'After filtering'})
title('Signal A(1,1,:)') Matt J on 26 Apr 2022
You can use ffts
kernel=reshape(gaussianProfile,1,1,[]);
N=size(Array,3)+size(kernel,3)-1;
F=@(z)fft(z,N,3);
invF=@(z)ifft(z,[],3,'symmetric');
kernel=reshape(gaussianProfile,1,1,[]);
output = invF( F(kernel).*F(Array) );

Matt J on 26 Apr 2022
Edited: Matt J on 26 Apr 2022
If you have the Image Processing Toolbox, you can use imgaussfilt3,
output = imgaussfilt3(Array,[.1,.1,sigma]);