Lot's of people think DSP is hard, it's not. If you can avoid getting bogged down in the math you'll be able to see it intuitively.
We normally use DSP to test analog devices. Signal to Noise measurements, stereo separation, DAC and ADC linearity, all kinds of stuff. The one device you don't use DSP to test? A DSP chip! These are usually pure digital, so you just run a lot of patterns to verify functionality.