Signal processing is often at a junction between applied statistics, numerical math, analytic math, physics, electronics and programming. Big data, visualization and machine learning may be overlapping skills. Depending on interest or requirements of your employer, you could end up designing new modem (algorithms) destined for an fpga, noise reduction algorithms for speech running on smartphones, or a new radar system for looking into the ice cover of one of the moons of Jupiter.
You could design and work with the low level circuitry of asic design, write assembly code for a quirky micro controller, spend your days writing high level numpy code or do calculations and white board design of systems for others to implement.