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I mentioned this in another thread, but how about an alarm clock -- sounds easy enough, but I'll throw in this piece of signal processing wonder: It will have some type of alarm that you synthesize. So you will have the PIC a DAC and glue logic. When the alarm time comes around, your pic will play the carillion (or whatever you choose) by outputting the digital samples through the analog network and your speaker. The trickery will be to make it sound good with the limited memory of the PIC.
My approach would be to scour the internet for a sound I would like as an alarm and then look at some techniques for squeezing audio into as few bits as possible without needing a full blown MP3 decoder.
I think for a senior project this has the right mix of theory, research, and implementation.