Signals, both continuous and discrete, have attributes that allow them to be classified into different types. Three broad categories of signal classification are periodic, aperiodic, and random.
Signals that repeat over and over are said to be periodic. In mathematical terms, a signal is periodic if
x(t + T) = x(t) (continuous-time)
x[n + N] = x[n] (discrete-time)
The smallest T or N for which the equality holds is the signal period. The sinusoidal signal of the following figure is periodic because of the mod2π property of cosine.
The signal has period 0.5 seconds (s), which turns out to be the reciprocal of the frequency f0 = 2 Hz. The square wave signal that follows in part (a) is another example of a periodic signal.
Signals that are deterministic (completely determined functions of time) but not periodic are known as aperiodic. Point of view matters. If a signal occurs infrequently, you may view it as aperiodic. The rectangular pulse of duration shown in part (b) is an aperiodic signal.
A signal is random if one or more signal attributes takes on unpredictable values in a probability sense (you love statistics, right?).
Here are two good examples of a random signal:
The noise you hear when you’re between stations on an FM radio. See a waveform representation of this noise in part (c).
Speech: If you try to capture audio samples on a computer of someone speaking the word hello over and over, you’ll find that each capture looks a little different.
Engineers working with communication receivers are concerned with random signals, especially noise.