Using Arduino audio to control an LED light I am looking for a way to control an LED on a circuit board using audio input for learning purposes. 

I have written my own speech recognition system using dynamic time warping in Python, but I would like to know if (and maybe what models if not all can do) Arduino can possibly handle the processing of a 70 by 70 O(n^2) matrix traversal with fft or dct operations on audio input divided into 10ms frames.

Any advice will be appreciated.
The Due or Tre may have enough power for this. The Yún may be able to offload it to the more powerful CPU. Every other Arduino will struggle with it.