I have found that the FFT library at http://www.arduinoos.com/2010/10/fast-fourier-transform-fft/
is quite good. While on an Uno this would be rather slow (hence all the FFT libraries for AVR written in assembler for speed), this version uses more time consuming math functions but with the increased speed of the Due this may be fine for many applications.
It compiles on Due with two changes:
1) In the library, somehow square is not defined in math.h. You can add #define square(x) (x*x) at the top of the library source
2) In the example, the code to blink an LED as an indicator is AVR specific. You can port it to pin 13 blinking with little effort or comment out the code and rely on the great Serial.print functions you can enable in the code.
I hope this helps.
Mike from http://21stdigitalhome.blogspot.com/