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:
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:
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).
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.
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.