Matlab N-D Simple Filtering Using Fourier Transforms

simple_conv.m

function convolved = simple_conv( Image, Filter )
% A simple Fourier Convolution Function written in matlab.
% It works on N-D arrays and N-D filters.

%%
% Dimensionality of input image
nDim = ndims( Image ); 


%% Make a filter the same size as the image
LargeFilter = zeros( size( Image ) );

expressionstart = 'LargeFilter(';
iterexp = '1:size(Filter,%i)';
for ii = 1 : nDim
    expressionstart = ...
        horzcat( expressionstart, ...
        sprintf( iterexp, ii ) );
    if ii ~= nDim
        expressionstart = ...
        horzcat( expressionstart, ...
        ',' );
    end
end
expressionstart = ...
        horzcat( expressionstart, ...
        ') = Filter;' );

eval( expressionstart );
LargeFilter(:) = circshift( LargeFilter, -1*floor(size( Filter )./2) );

%% FFT convolution

% Forward Fourier Transform
convolved = fftn( Image );
% Multiply in the Fourier Space
convolved(:) = convolved.* conj(fftn( LargeFilter ));
% Inverse Fourier Transform
convolved(:) = ifftn( convolved );