How to check if a signal is power signal or energy signal?
let's assume the signal, $x(t)$ is not identically zero for all $t$.
an &quot;energy signal&quot; (what i would prefer to call a &quot;finite energy signal&quot;) is such a signal, $x(t)$ with a finite energy:
$$ 0 \ &lt; \ \int_{-\infty}^{\infty} |x(t)|^2 \ dt \ &lt; \ +\infty $$
BTW, sometimes for mathematical ease, we require a stricter sense of finite &quot;energy&quot;:
$$ 0 \ &lt; \ \int_{-\infty}^{\infty} |x(t)| \ dt \ &lt; \ +\infty $$
and a &quot;power signal&quot; (what i would prefer to call a &quot;finite power signal&quot;) is such a signal, $x(t)$ with finite power:
$$ 0 \ &lt; \ \lim_{T \to +\infty} \frac{1}{T}\int_{-\frac{T}2}^{\frac{T}2} |x(t)|^2 \ dt \ &lt; \ +\infty $$
i think that is the most fundamental definitions of the two classes of continuous-time signals.  you can do a very similar definitions for discrete-time signals, $x[n]$.