An LVDT is a transformer that is excited with a sinewave. Mechanical motion affects the coupling of the signal on the primary onto the secondary. It can be used to measure distances on the order of nanometers. This precision is commonly required on grinding machines.
Good idea about suggesting a LVDT, it's a nice application that gives good visual feedback on what is being accomplished by the DSP processing.
We used long LVDT to measure travel on a linear actuator with a 12" stroke. It is amazing how accurate they can be. You excite the LVDT via it's primary winding with an AC voltage and by reading the phase and amplitude of the two secondary windings you can determine absolute position with very good precision. That would be a good application of DSP capabilities if you can find an affordable LVDT to play with.