There has to be some way.
There is. Pick the right hardware. The Arduino is based on the ATmega328. The ATmega328 is a microcontroller
. You are looking for a microprocessor
You are looking to do DSP (Digital Signal Processing) with your Arduino, which is a lousy platform for DSP. From a hardware perspective 2k of SRAM just isn't enough even for what you are trying to do.
You might want to look at something like the Maple platform (http://leaflabs.com/
). Similar to Arduino is concept but is based on a ARM 32-bit processor.