Classification of measurement signals

A measurement signal is the physical or electrical quantity carrying information about the measurand. Signals are classified in several ways.

Static and dynamic

• Static signal: does not change with time, or changes very slowly. Example: the weight of an object on a scale, dead-load pressure.
• Dynamic signal: varies with time. It may be steady-periodic, aperiodic or transient. Example: engine vibration, pressure in a cylinder.

Deterministic and random

• Deterministic: can be described by a mathematical function of time and predicted exactly. Example: $x(t) = A\sin\omega t$.
• Random (nondeterministic): cannot be predicted; it can only be described statistically by its mean, variance and probability density. Example: turbulent wind velocity, noise.

Periodic signals

• Simple periodic (harmonic): a single sine or cosine at one frequency, $x = A\sin(\omega t + \phi)$. Example: the 50 Hz mains voltage.
• Complex periodic: repeats after a period $T$ but contains many harmonics, $x(t) = x(t+T)$. Example: a square wave from a rotating machine, which has a Fourier series.

Aperiodic and transient

• Almost periodic: a sum of harmonics whose frequency ratios are not rational, so the signal never exactly repeats. Example: $x(t) = \sin t + \sin\sqrt{2}\,t$, such as the vibration of a machine driven by two shafts at unrelated speeds.
• Transient: exists for a short time and then dies away. Example: a step input, the impulse from a hammer blow, decaying vibration after an impact.

 Signals
  |-- Static
  |-- Dynamic
        |-- Deterministic
        |     |-- Periodic (simple, complex)
        |     |-- Aperiodic (almost periodic, transient)
        |-- Random (stationary, non-stationary)