Implement 2D Discrete Fourier Transform?

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tn0432
tn0432 2015-1-19
回答： Subeesh Vasu 2018-2-26
Hello, I try to implement Discrete Fourier Transform (DFT) and draw the spectrum without using fft function.
The problem is that the calculation of DFT taking too long. Do you have any ideas to increase the calculation speed?
Please find the tested image at https://www.dropbox.com/s/vk9o5cpxjr0dyhc/cameraman.tif?dl=0 ! Thanks
Img=double(imread('cameraman.tif'));
[Img_M, Img_N] = size(Img);
Output=zeros(Img_M,Img_N);
SumInner = 0;
SumOutner = 0;
%%2D Discrete Fourier Transform
for u = 1:(Img_M-1)
for v = 1:(Img_N-1)
for x = 1:(Img_M-1)
for y = 1:(Img_N-1)
SumInner = SumInner + Img(x,y) * exp(-1i*2*3.1416*((u*x/Img_M)+(v*y/Img_N)));
end
SumOutner = SumOutner + SumInner;
end
Output(u,v) = SumOutner;
SumOutner = 0;
SumInner = 0;
end
end
%%Calculate Spectrum and show
Output2 = zeros(Img_M,Img_N);
for u = 1:(Img_M-1)
for v = 1:(Img_N-1)
Output2(u,v) = sqrt((real(Output(u,v))^2+imag(Output(u,v))^2))/1000000;
end
end
imshow(Output2)

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回答（3 个）

Subeesh Vasu
Subeesh Vasu 2018-2-26
Img=double(imresize(imread('cameraman.tif'),0.3));
[Img_M, Img_N] = size(Img);
Output=zeros(Img_M,Img_N);
SumOutner = 0;
%%Centralized 2D Discrete Fourier Transform
[nx,ny]=ndgrid([0:Img_M-1]-(Img_M-1)/2,[0:Img_N-1]-(Img_N-1)/2 );
du=1;
for u = [0:Img_M-1]-(Img_M-1)/2
dv=1;
for v = [0:Img_N-1]-(Img_N-1)/2
SumOutner=sum(sum(Img.*exp(-1i*2*3.1416*(u*nx/Img_M+v*ny/Img_N))));
Output(du,dv) = SumOutner;
dv=dv+1;
end
du=du+1;
end
%%Calculate Spectrum and show
imshow(uint8(abs(Output)/60))
Image Analyst
Image Analyst 2015-1-19
Well you got x and y reversed. It should be Img(y, x), NOT Img(x,y). Don't agree? Just think about it and you should have a forehead slapping moment.
And your loops, like over u and v should have the left most index be the innermost for loop .
reetika dash
reetika dash 2017-9-5
编辑：reetika dash 2017-9-5
if true
% code
endImg=imread('cameraman.tif');
%Img=mat2gray(Img);
[x,y]=size(Img); subplot(1,2,1); imshow(Img); Img=double(Img);
A=zeros(x,y); for i=1:x for j=1:y A(i,j)=exp((-1*1j*2*pi*j*i)/x); end end %output=zeros(80,80); Output=A*Img*A'; Output=fftshift(Output); Output2 = zeros(x,y);
for u = 1:x
for v = 1:y
Output2(u,v) = sqrt((real(Output(u,v))^2+imag(Output(u,v))^2));
end
end
%Output2=fftshift(Output2);
subplot(1,2,2);
imshow(mat2gray(log10(1+Output2)))

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