How to implement the faster than fast fourier transform in cvx

This is the first time that I use the cvx and I want to implement the newest fast fourier transform proposed MIT students( http://web.mit.edu/newsoffice/2012/faster-fourier-transforms-0118.html ), and I don’t know how to begin.
does anyone have an idea?

It does not strike me that CVX is an appropriate tool for this type of work.