For an exam we have to calculate Fourier Transform by hand in complex space and in $\mathbb{Z}_{32}$ space ($\mathbb{Z}$ mod 32). I am familiar with recursive algorithm in a complex space (example in an image bellow, butterfly operations), but I have no idea how to do it in a $\mathbb{Z}_{32}$ space. ($\mathbb{Z}$ are integers both positive and negative).
Given polynomial for $\mathbb{Z}_{32}$ is: $$p(x) = -3x^6 + 4x^5 -x^4-3x^2+6x-1$$ Additional, smallest primitive root of unity should be taken.
Can someone please explain the procedure and what primitive root of unity really represents?
