Answer:
The energy signal is a signal that has energy only in a finite time, not all the time. And as we know, the power of a signal is the speed of its energy over time ... that is (energy / time). So, in the energy signal (power = energy (finite) / time (infinite) [at all times]) that is equivalent to ZERO
Power Signal is a signal that has a finite power (not equal to ZERO) ... and as we said earlier that (power = energy / (infinite) time [at all times]). So, the energy is very very large that tends to infinity
Step-by-step explanation:
E = ∫V2 (t) Rdt
if V (t) = x (t)
and R = 1Ω
E = ∫V2 (t) dt
The energy and power expression is expressed as a normalized expression (calculated at R = 1Ω)
The energy of a signal (complex or real) is given by
E = ∫∞ - ∞ | x2 (t) | dt
The power of a signal (when it is periodic) is given by
P = 1T∫T | x2 (t) | dt
The power of a signal (when it is not periodic) is given by
P = limT → ∞1T∫T2 - T2 | x2 (t) | dt
POWER SIGNALS
⇒ A signal is said to be an energy signal if it has a finite amount of associated energy.
E → finite
P → 0
⇒ A signal will have a finite amount of energy if it is absolutely integrable
∫∞ - ∞ | x (t) | dt <∞
Example 1
x (t) = e - atu (t)
go> 0
∫∞0e - atdt = 1a⇒
Energy signal
E = ∫∞ - ∞e - 2atdt = 12a
Example 2
x (t). = e - a | t |
go> 0
x (t) = e - atu (t) eatu (−t)
go> 0
∫∞0e - atdt ∫0 - ∞eatdt = 1st 1a⇒
Energy signal
E = ∫0 - ∞e2atdt ∫∞0e - 2atdt = 12a 12a = 1a
Example 3
x (t) = eatu (t)
go> 0
∫∞0eatdt → ∞⇒
It is not an energy signal
Example 4
x (t) = Au (t)
∫∞0dt → ∞⇒
It is not an energy signal
Example 5
x (t) = sin (ω0t)
∫∞ - ∞ | sin (ω0t) | dt → ∞⇒
It is not an energy signal