MATLAB: Low-pass exponential filter – fourier space

fourier spaceifftshift functionlow-pass filter

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

Best Answer

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.
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