Let x,y be finite real valued sequences defined on 0...N-1 and let g be a non negative integer .
also on 0..N-1.
In addition, the DFT of y is known in closed form.
Is there a way to write z as some cyclic convolution, so that with the help of the convolution theorem z can be calculated in NLOG N istead of N^2?
I tried following the convolution therem proff but i get stuck:
The problem is that the second sum depends on k so the double sum doesn't factor to the product of DFTs.
what am I missing?