Unfortunately, there is a big difference in scale between a microcontroller and a general-purpose computing device.
Storing one second of 8bit monophonic 8KHz audio (radio quality) would take 8x the RAM in the Arduino. There is a companion board called the Adafruit Wave Shield which lets you store such sound samples as WAV files on a plain SD media card, and pipe it out to an audio jack without any processing.
Doing a fast-fourier transform on sound data ON THE BOARD seems unlikely, both for speed and capacity reasons.
