MATLAB: Transform a D-4 Array to generate a real valued ifftn

arrayreal valued ifftnshape

Hi I want to appy a 4 dimensional filter to a noise array. Abterwards I would like to generate the real valued IFFTn of the array. My solution at the moment is
N=randn(length(x),length(y),length(z),length(t));   %white noise array
FN=fftn(N);                                         %Fouriertransform of white noise
kernel=zeros(length(x),length(y),length(z),length(t));
 for i=1:length(x)
    for j=1:length(y)
        for k=1:length(z)
            for l=1:length(t)
                if kernel(i,j,k,l)==0   %check if entry is already set
                kernel(i,j,k,l)=FN(i,j,k,l)*(kx(j)^2+ky(k)^2)/(kx(i)^2+ky(j)^2+kz(k)^2)/(alpha^2*(kx(i)^2+ky(j)^2+kz(k)^2)+1i*kt(l)); 
                    if i==1||j==1||k==1||l==1  
                        %do nothing first entires aren't mirrored
                    else
                        kernel(length(x)-i+2,length(y)-j+2,length(z)-k+2,length(t)-l+2)=conj(kernel(i,j,k,l)); %mirror the entries
                    end
                else
                end
            end
        end
    end
end
Using these loops takes a lot of computation time so I tried
[KX,KY,KZ,KT]=ngrid(kx,ky,kz,kt);                                                  %Generating grid
KERNEL=(KX.^2+KY.^2)./(KX.^2+KY.^2+KZ.^2)./(alpha.^2.*(KX.^2+KY.^2+KZ.^2)+1i.*KT); 
kernel2=FN.*KERNEL;
Is there a simple solution to bring 'kernel2' into the desired shape, that
  • for all i,j,k,l>1
  • kernel(i,j,k,l)=conj(m_x-i+2,m_y-j+2,m_z-k+2,m_t-l+2)
  • is true for all entries,
  • with m_n=length(n), n=x,y,z,t Best regards

Best Answer

You should just do
ifftn(kernel,'symmetric')
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