2.1c Signal Periodicity

Periodicity of Signals

A continuous-time signal $x$ is said to be periodic if there is a real number $p>0$, such that
$x(t+p)=x(t)\text{for all }t.$
The smallest $p$ for which the above equation holds is called the fundamental period of $x$. The fundamental frequency of $x$ is denoted by
$w_0=\frac{2\pi }{p}.$

Additionally, all periodic discrete-time signals share a fundamental period $p=1$, as well as a fundamental frequency ${\omega }_0=2\pi$.

Note 1 (Constant Signals) ${\omega }_0=0$.

Constant signals (i.e. DC signals) have an undefined period and a fundamental frequency

Note 2 (Compound Signals) $x$ is formed by combining several periodic signals, its overall period is the least common multiple of their individual periods.

If a signal