(Digital) Signal-processing is a very broad field, but very powerful and important in modern communications systems.

As examples, you get audio signal-processing for lossy compression (bit-rate-reduction) and echo-cancellation and speech-recognition, and signal processing of radiofrequency signals in any "digital"-mode transmitter or receiver such as mobile phone or DAB radio or digital-TV (take a deep breath and look up OFDM :-) ).

It's amazing how Fourier transforms invented (or perhaps "discovered") by Joseph Fourier 200 years ago are at the heart of so much of modern technology.