# low-pass exponential filter - fourier space

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Aude Rapet on 27 Oct 2016
Hello,
I am a beginner in Matlab and I have to understand a code. The part I don't understand is to calculate filter for displacement datas (in Fourier space) (low-pass exponential filter).
qmax=nr2/(pi*min_feature_size); %min_feature_size: spatial resolution of the stress measurement in units of the grid spacing.
%nr2=number of rows and columns across field (must be square)
% Get distance from of a grid point from the centre of the array
y=repmat((1:nr2)'-nr2/2,1,nr2);
x=y';
q=sqrt(x.^2+y.^2);
% Make the filter
qmsk=exp(-(q./qmax).^2);
qmsk=ifftshift(qmsk)
I have difficutlies understanding what he is doing exactly...what is the iffshift for? and what is this filter doing excalty
Thank you for your help Aude

David Goodmanson on 27 Oct 2016
Hi Aude, To construct a filter in this situation it's convenient to use a frequency array with zero frequency in the center. In one dimension the lowpass filter might look like
f = -50:49; y = exp(-f.^2/100); plot(f,y)
(it's more properly called a gaussian than an exponential). But to do an fft or an ifft, Matlab wants zero frequency at the beginning of the array, not the middle. The ifftshift function swaps halves of the y array to put zero frequency at the beginning. So
ff = 0:99; plot(ff,ifftshift(y))
puts the center of the gaussian down at zero frequency, and the negative frequency part of the gaussian into the upper half of the frequency array. Your code does the same in two dimensions.

David Goodmanson on 3 Nov 2016
Hi Aude, looking at my previous comment, I didn't mean to imply that the Mathworks site is strictly for 100% Matlab procedural questions. Sometimes good questions come up about what Matlab is doing in a piece of code. It's just a case of striking the right balance of what is related to Matlab and what is independent of it.
Aude Rapet on 4 Nov 2016
Yes I understand.
I just have another question, are you sure is it a gaussian low-pass filter? As there isn't the normalizing factor (1/sqrt(2*pi)*σ), and neither the Sigma which set the width of the gaussian function...?
As they just do : qmsk=exp(-(q./qmax).^2)
Is is possible to "create" a filter like this? I mean without using a known one like Gaussian, Butterworth,...
I do understand that the goal of a low-pass filter but I am confused with the one of my code... Thank you!
David Goodmanson on 4 Nov 2016
It is a gaussian filter, because you can write it as exp( -(q.^2) / (qmax^2) ). Then if you define sigma in terms of qmax with the expression 2*sigma^2 = qmax^2, you get same formula for a gaussian as in one of your earlier comments. Except for the normalizing factor in front. Again, I don't know why the are not using that.