Well how much processing grunt do you need - what approach are you going with? Certainly a 32 bit
Arduino would be a start, for FFT one with hardware floating point would be really good to have.
To implement digital filtering in fixed point doesn't require floating point, but 32 bit hardware multiply
operation is really good to have, as digital filtering is all multiply-and-add.
Have you looked for existing projects that might have tackled similar / same problem?