What is a norm that can measure average oscillatory amplitude?

What is a norm that can measure average oscillatory amplitude?

I am numerically computing the growth of an oscillatory instability in a
fluid system. Suppose for simplicity that the function $f(x)$ [defined on
a finite interval] has oscillations of different modes and different
amplitudes, but is otherwise centered about $f = 0$.
As a measure of the growth of the oscillations, I have been numerically
computing maxes and mins, and then averaging the heights. So for instance,
$$ \text{Average oscillations} = \frac{1}{N} \sum_{j=1}^N
f(x^\text{max}_i), $$
where $x^\text{max}_i$ are the locations of the $N$ maxima within the domain.
Is there an easier way to measure this notion of average oscillatory
height? Are there other norms that might work to give us a 'feel' for the
value?
What if $f(x)$ is not centered about zero? Suppose that $f(x) = x +
\cos(x)$. I'd like to say that the average heights of the oscillations are
one---assuming the oscillations are closely spaced, then I can just
compute the distance between max and min values, but again, this requires
me to code an automatic extrema-finding routine. Is there an easy norm to
apply for this case as well?
I am hoping that there might be some commonly used norms (e.g. in fields
like signal processing).