Question 1: In Figure 1, explain why there are strong bands in the frequency dom

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Question 1: In Figure 1, explain why there are strong bands in the frequency domain, Part 2: Implement a 2-D Fourier Transform Your task for today is to implement a 2-D Fourier transform. The 2-D Fourier transform is ined as: F(u,v) = MN However, because the Fourier transform is separable, you can carry out two 1-D Fourier ansforms: first in the x-direction, then again in the y-direction: F(u, v)e Implement the Fourier transform using both forms and show that the results are the same. Carry to verify use the mandrill.gif image from previous labs. Include your code in your lab report. Include the result of your Fourier transforms in the lab report. Question 2: Waly would you want to compute the Fourier Transform separately?

Explanation / Answer

Matlab Code

N=30;M=40;
u=80;v=70;
for x=1:M
for y=1:N
f=x+y;
F=f*exp(-2*pi*i*(u*x/M+v*y/N));
end
end
F=F/M*N
N=30;M=40;
u=80;v=70;
for x=1:M
for y=1:N
f1=x+y;
F1=f1*exp(-2*pi*i*(v*y/N));
end
F2=F1*exp(-2*pi*i*(u*x/M));
end
F2=F2/M*N
% Clearly F and F2 have the same value

We want to compute the Fourier transform seperately because for fast speed nature of FFT than discrete Fourier transform.And to composite into smaller parts like divide and conquer algorithm which will help the nature of speed of Fast Fourier Transform.

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