FFT Using Pic Microcontroller
Microchip has a whole line of PIC microcontrollers with DSP capabilities, aptly named dsPIC.  They are essentially PIC24 micros with DSP features added, including:

hardware multiply–accumulate (MAC)
barrel shifting
bit reversal
hardware support for loop indexing


There are several code examples using dsPICs for doing FFT, such as this one.

Here is an article describing how to use a dsPIC33 to display FFT on an LCD display. 

You can find many more resources by Googling for:

dspic fft microchip library