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

When I transform an image from the spatial domain to the frequency domain, some frequencies are negative. What is the meaning of the negative sign?

For example: • The numbers in the matrix 'b' are not frequencies but amplitudes at specific frequencies. – pichenettes Jan 5 '14 at 16:19
• so, what does it mean?! – Mohammad Hyari Jan 5 '14 at 16:36
• a phase shift of 180° for the corresponding frequency – sellibitze Jan 5 '14 at 22:04

## 3 Answers

Each DCT output bin is a (weighted) correlation against a cosine function of a certain frequency. 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).

• Yes, it's all about the phase. – Jim Clay Jan 5 '14 at 21:20
• @hotpaw2 Hello, I have seen that the Correlation term is used in order to explain the Negative frequencies concept. Thank you for sharing that,but is it possible please to provide some more references en lighting us on why that stands? I have only used correlation,in simulations i was running on a CDMA system,i am trying to understand how is related to the fourier (while it is multiplication on the freq domain while correlation on the time),without being really keen on the maths behind :D and had no particular progress so far... Much appreciated a constructive feedback. – Giwrgos Rizeakos Feb 3 '14 at 16:04

The matrix b is the same size as a and contains the discrete cosine transform coefficients indicating the correlation between the cosine function at two specific frequencies. They are not necessary to be positive values. The dimension, 4*4 in your case, represents the different frequencies.

• thanks alot, but i'm asking about the negative sign – Mohammad Hyari Jan 5 '14 at 16:45
• yes i was talking about the sign. They just mean the negative coefficients, not the frequency. – lennon310 Jan 5 '14 at 16:49

Consider a 1-D delta function. It can be written as difference of two unit step trains. All we have done is represent one data in terms of another - mathematically, we are using a different set of basis vectors for representing same data. d(n) = u(n) - u(n-1) Similarly, in the DCT, one is trying to express some data in terms of a different basis vector set - the set of cosine functions. And just like in any general vector space, some of the coefficients might be negative. There is no other real great physical significance to this.