Signals — both continuous-time signals and their discrete-time counterparts — are categorized according to certain properties, such as deterministic or random, periodic or aperiodic, power or energy, and even or odd. These traits aren't mutually exclusive; signals can hold multiple classifications.
Here are some of the most important signal properties.
But wait! There's more. Signals can also be categorized as exponential, sinusoidal, or a special sequence. The unit sample sequence and the unit step sequence are special signals of interest in discrete-time. All the continuous-time signal classifications have discrete-time counterparts, except singularity functions, which appear in continuous-time only.
Defining special signals that serve as building blocks for more complex signals makes the creation of custom signal models to suit your needs more systematic and convenient.