The ADC in the 16MHz Arduinos (Uno, Mega, Leonardo) can only do about 15,000 samples per second at max resolution and up to 76,000 at lower resolution so I suspect they would not be capable of the frequency analysis.
And it could be that when working at a high sample rate there would not be spare capacity for other tasks.
A RaspberryPi might be better for that part of the project. It may be able to do the other tasks as well.
...R