Where can I find Digital Filter Examples?
AN219 - Using Microcontrollers in Digital Signal Processing Applications shows examples of digital filters, Goertzel Algorithm for DTMF detection, and FFT implementation on general purpose microcontrollers. The peripheral emphasized in this application note is the on-chip 2-cycle MAC unit available in the 'F36x and 'F12x family of microcontrollers.
Other application notes that may be of interest are:
AN142 - FFT Routines for the C8051F12x Family
AN218 - DTMF Decoder Reference Design
Application notes can be downloaded from https://www.silabs.com/products/mcu/Pages/ApplicationNotes.aspx.