Doing audio processing with DFT on a microcontroller
Generally, Arm Cortex-A9 type processor can be used for Audio signal processing blocks for effective results. For your case, basic arm processor type can support common floating point operations without any external floating point unit.
But, in case of special floating point operations like saturation,rounding and truncation, you shall use some advanced arm processors like cortex-a9 which has specific floating point unit for efficient signal processing.