EE4206/EE5806 Digital Image Processing : Assignment Q3
3. An FFT computer program is available for computing the DFT of 1D real data.
(a) Show how such a program could be used to compute the DFT of 1D complex data.
ans : by using Euler's equation : e^-jx = cos(x) - jsin(x), the real part is cos(x), the imaginary part is -jsin(x).
First, we square the real part , ie., cos^2(x).
Second, use 1 to minus it. 1 - (cos^2(x) ).
Since cos^2(x) + sin^2(x) =1, therefore, 1 - cos^2(x) = sin^2(x). We then take the square root and negate it, this is the imaginary part of the DFT.
j = sqrt( sin^2(x) );
j = sin(x);
j = -sin(x);
(b) Show how such a program could be used to compute the DFT of a 2D digital image whose pixels are real numbers. (20 marks)
ans : The 2-D DFT of f(x,y) can be obtained by computing the 1-D transform of EACH row of f(x,y) and then computing the 1-D transform along EACH column of the result.
簡明宇：香港高等教育為誰而設？" 國際化 " 實為 " 國內化 "
周易象義弁正 -- 根本通明著