Yuor project doesnt seem to be outside the capabilities of a decent high-speed microconverter, audio frequency input/output should be ok, where you might have problems is the speech processing. does it have to be in real time? if not, the mico is fine, if not it could struggle, depending on the level of processing.
Selecting a processor with a high clock speed and, in my opinion, this is the vital part, fast multiplication. CYGNAL parts seem to be cheap and multiplications only require 4 clock cycles and the divisions only take 8 clock cycles. As the max clock frequency is 25MHz, it has quite a bit of processing power.