You can find an introduction to signals here. This post is part of a series on Image and Signal Processing.

If you are looking for the *power* of a signal, you may read the dedicated note. Now, let’s dive into the energy of a signal to better understand it.

## Energy of a signal

The energy of a signal is defined mathematically as:

Note that in the latter case $|f(t)|^2 = f(t) \bar{f(t)}$, where $\bar{f(t)}$ is the complex conjugate of $f(t)$.

The definition thus varies slightly depending on the type of signal: the ways you compute the energy of real signals and complex signals are a little different. You may want to read more about complex numbers.

A signal is said to be an energy signal (or with finite energy) if the integral $E_f$ converges and is not $0$.

- This condition is sufficient to ensure that $f$ has a Fourier Transform (though it is not necessary).
- It tends to $0$ to infinity: $\lim_{t \to \infty} f(t) = 0$.
- Energy is measured in Joules [J].

If
$f$ is a power signal then it *cannot* be an energy signal (and vice-versa).
Some signals are not power nor energy signals — so beware!