Question

Categories each of the following signals as an energy signal or a power signal and find the energy:
xt={ t, 0≤t≤ 1 2-t, 1≤t≤2 0, Otherwise

Answer 1

Answer:

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

an "energy signal" (what i would prefer to call a "finite energy signal") is such a signal, x(t)x(t) with a finite energy:

0 < ∫∞−∞|x(t)|2 dt < +∞0 < ∫−∞∞|x(t)|2 dt < +∞

BTW, sometimes for mathematical ease, we require a stricter sense of finite "energy":

0 < ∫∞−∞|x(t)| dt < +∞0 < ∫−∞∞|x(t)| dt < +∞

and a "power signal" (what i would prefer to call a "finite power signal") is such a signal, x(t)x(t) with finite power:

0 < limT→+∞1T∫T2−T2|x(t)|2 dt < +∞0 < limT→+∞1T∫−T2T2|x(t)|2 dt < +∞

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]x[n].