PeterH:
My suggestion is that the right board for DSP is not an Arduino.
My suggestion would be to agree with that and add "including Due".
Put it like this. My DAW runs on a 3.4 GHz Intel i7 with 8GB DDR-3. It does 'near realtime' audio DSP, which means that when recording and mixing it uses a reasonably high quality mode, and during final mixdown it uses a non-realtime best quality mode.
Of course, it depends on exactly what you want to do and how low you can put your quality requirements.