How do I do a Fourier Transform of a 2D Matrix? Specifically, for the space-domain filter given...

Question

How do I do a Fourier Transform of a 2D Matrix? Specifically, for the space-domain filter given below (assuming the origin is at the center), how do I find its Fourier transform? I was told to make use of the separable property of the filter whenever appropriate. The final form of the Fourier transform should contain trigonometric functions and real numbers only (no complex exponentials). Please help.

H=[ XXXXXXXXXX; XXXXXXXXXX; XXXXXXXXXX]

Robert · Accepted Answer

Fourier Transform of 2D Matrix
Question:   How do I do a Fourier Transform of a 2D Matrix? Specifically, for the 
space-domain filter given below (assuming the origin is at the center), how do I 
find its Fourier transform? I was told to make use of the separable property of the 
filter whenever appropriate. The final form of the Fourier transform should contain 
trigonometric functions and real numbers only (no complex exponentials). Please 
help. 
H=[-1 -1 -1; -1 8 -1; -1 -1 -1] 
Solution: 
H= [
      
     
      
]
Fourier Transform of 2D matrix is calculated as follows:

How do I do a Fourier Transform of a 2D Matrix? Specifically, for the space-domain filter given below (assuming the origin is at the center), how do I find its Fourier transform? I was told to make...

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