When you start to think of any stream of numbers as a digital signal, a lot of the techniques become useful. For example, user interfaces provide a fairly high-resolution stream of quantifiable user events, like touch positions. Often you want to smooth these in specific ways. If you understand how a low-pass filter works, this is easy.
Any tips on where / how to start? Which books / tutorials worked for you? My background is in software engineering and the only thing I know about DSP is a very very basic understanding of the Fourier transform :)