# What are the conditions for a signal to be an energy signal and a power signal?

I know how to find the power and the energy of a signal. What I have a problem with is knowing whether a signal is an energy signal or a power signal.

According to my teacher, a signal is a power signal if its power is finite (less than infinity) and non-zero and a signal is an energy signal if its energy is finite (less than infinity). What he does not specify is what happens if the energy of a signal is 0 such as in the case of the signal x(t) = 0.

The energy is obviously 0. Is this signal considered an energy signal or the signal x(t) is not considered a signal at all since its zero?

Furthermore, is it possible for a signal to be neither a power signal nor an energy signal?

Thank you.

I don't think that this line of thought is going to help you much.

signal [sig-nl]
Electronics. an electrical quantity or effect, as current, voltage, or electromagnetic waves, that can be varied in such a way as to convey information. Source: Dictionary.com.

In most cases some power will be required to pass the information but that is inherent in the way electronics works and it doesn't mean that power is a signal.

In contrast power suggests providing energy to a device with no information transmitted.

The energy is obviously 0. Is this signal considered an energy signal or the signal x(t) is not considered a signal at all since its zero?

I would think that zero indicates a lack of power or signal. It's nothing.

Furthermore, is it possible for a signal to be neither a power signal nor an energy signal?

We're back to the definitions again. If it's a signal then it's a signal.

That logic specifies that x(t)=0 cannot be a "power signal" (assuming x is power or energy over time). This is thanks to the non-zero requirement.

Funny thing about energy is that while we generally work in some absolute numbers, energy is relative. In order to say something has X energy at a state, there must be a theoretical state that we consider to be 0 energy, from which it would require X work in order to reach the state of something. In other words, energy and work are not the same, and energy can also be allowed to go negative in describing the state. energy(t) = 0 can describe the same existence as energy(t) = 1 compared to some other state.
Think gravitational potential energy where a mass lower than your zero state can be treated as a negative state. You may be thinking of things like kinetic energy which is proportional to the square of a speed. Realizing that the speed term is based on velocity in some inertial reference frame, that there exist other potential inertial reference frames, and that velocity is directional can lead to some interesting areas of physics.

In reality, it is very difficult to come up something that is not an energy signal. Even if you have a massive energy source supplying power for a very long time, and it is useful to model as infinite energy (finite power over an infinite time), that remains an approximation; we have managed to theoretically bound every power source discovered thus far.