What does the negative sign mean in the image frequency domain?

A negative value would represent a negative correlation, e.g. something in the image data is of the opposite phase to that cosine (e.g. maybe dark when the cosine is 1, and light when the cosine is -1, instead of vice-versa for a positive correlation).

1. What does negative frequency represent?
2. What do negative values in FFT mean?
3. Why is the negative sign in Fourier transform?
4. Why does FFT have negative frequency?

What does negative frequency represent?

Negative frequency is an idea associated with complex exponentials. A single sine wave can be broken down into two complex exponentials ('spinning numbers'), one with a positive exponent and one with a negative exponent. That one with the negative exponent is where you get the concept of a negative frequency.

What do negative values in FFT mean?

Negative values in the real component of the result of a complex FFT correspond to a negative correlation with a cosine waveform (same as a 180 degree phase shift). If you want to check the energy at each frequency, graph the magnitude (sqrt(rere+imim)) of each complex FFT result bin.

Why is the negative sign in Fourier transform?

The Fourier transform has a negative sign to intentionally rotate in the opposite direction as the frequencies that they are "looking" for.

Why does FFT have negative frequency?

The reason is that the Fourier transform is symmetric about the y-axis, because the Fourier transform is mathematically defined on the interval (-Inf,Inf). The actual Fourier transform therefore has negative frequencies.