How to check if a signal is power signal or energy signal?

What is the procedure to check the signal type?

example:

$ x(t) = A \sin (\omega t) $

$ y(t) = A e^ {-\lambda |t|} $

Answer

let's assume the signal, $x(t)$ is not identically zero for all $t$.

an "energy signal" (what i would prefer to call a "finite energy signal") is such a signal, $x(t)$ with a finite energy: $$ 0 \ < \ \int_{-\infty}^{\infty} |x(t)|^2 \ dt \ < \ +\infty $$

BTW, sometimes for mathematical ease, we require a stricter sense of finite "energy": $$ 0 \ < \ \int_{-\infty}^{\infty} |x(t)| \ dt \ < \ +\infty $$

and a "power signal" (what i would prefer to call a "finite power signal") is such a signal, $x(t)$ with finite power: $$ 0 \ < \ \lim_{T \to +\infty} \frac{1}{2T}\int_{-T}^{T} |x(t)|^2 \ dt \ < \ +\infty $$

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, $x[n]$.