Help with Homework Problem for Img Processing class

Question

I have this homework about Image Processing:

1. Give the general equation of a complex or real-valued digital image that produces a delta function in the frequency domain.
2. Demonstrate this function for an image of size 8×8. Make sure to center the fft magnitude display using log(1+abs(fftshift(fft2(img)))).
3. Also, to establish that the complex part is zero, you can use max(abs(imag(fftimg(:)))).

I'm very lost and it is due tomorrow.

Does anyone have ideas about how to solve this problems?

I kinda understand part 1. He wanst me to find a function that, once Fourier transformed, we get a Delta function (like the Dirac Delta Function). But I have no idea about how to get such a function.

Thanks.

Answer 1

A constant function! That's a function that after FFT results in a delta function.

The part b is used to center the transform (just like multiplying the function by (-1)x+y).