Build a dual slope A/D converter. Quantify it’s performance.
Build a cardiotachometer – a device that measures pulse rate. The signal from the heart can either be from an ECG (electrical) source, or from a light source (measuring light transmission through skin)
Anadigm® makes a field programmable analog array that allows for dynamic synthesis of analog circuits (much as an FPGA does for digital circuits). This might be useful as a general purpose signal conditioner – or perhaps used with a genetic algorithm for analog circuit design.
Do something with a small FPGA package (in a USB dongle).