converting from conv2 to fft2

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mathango 2016-5-16

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/284473-converting-from-conv2-to-fft2

Does any one knows how to convert the following code into 2D and 3D version?

if true 
                                % 1D algorithm 
x = rand(1e5,1);
y = rand(1e5,1);
tic, z1 = conv(x,y); toc
n = length(x) + length(y) - 1;  
tic, z2 = ifft(fft(x,n) .* fft(y,n)); toc
disp(max(abs(z1-z2)./abs(z1)))      
                                % 2D algorithm with 'same'  
x = rand(1e4,1e4);
y = rand(1e2,1e2); 
tic, z1 = conv2(x,y,'same'); toc
n = length(x) + length(y) - 1;  
tic, z2 = ifft2(fft2(x,n) .* fft2(y,n)); toc
disp(max(abs(z1-z2)./abs(z1)))             
                                % 3D algorithm with 'same'   
x = rand(1e3,1e3,1e3);
y = rand(1e2,1e2,1e2); 
tic, z1 = convn(x,y,'same'); toc
n = length(x) + length(y) - 1;  
tic, z2 = ifftn(fftn(x,n) .* fftn(y,n)); toc
disp(max(abs(z1-z2)./abs(z1)))
end