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What effect does the brightness have on the frequency spectrum of 2D Fourier Transformation?

Example. Suppose we have a gray image and calculate 2D Fourier Transformation. Then we increase the brightness of the same image for 10% and repeat 2D Fourier how does the frequency spectrum change compare to the first one?

If I understand correctly only phase would change not frequency. Is that correct?

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If I understand correctly only phase would change not frequency. Is that correct?

Assuming "increasing brightness by 10%" just means multiplying each pixel's value with 1.1:

No, the phase won't change either. Since the Fourier Transform is a linear operation, you just multiply every point in the spectrum by the same factor. That doesn't affect phase, since 1.1 is a real number.

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No, only the amplitude would change. Changing brightness is nothing more than adding (or removing) offset to RGB or luma channel. As it only changes the average value of image, it only changes the DC component of fourier transform.

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