I looked up the sparse FFT, which this is about. It looks like a nice transform, but I think this article misrepresented it a bit. The article makes it sound like they found a new, much faster alternative to the FFT. In fact, their algorithm allows you to compute a limited part of the spectrum if you know the signal is sparse in the frequency domain. Most of the uses for the FFT are not sparse, so this is a special-purpose transform.