You could transpose it (effectively making the y-axis non-linear, or you can think it as a form of companding).
Assuming the signal is within the range [-1, 1].
One popular quick and simple solution is to simply apply the hyperbolic tangens function (tanh). This will limit values to [-1, 1] by penalizing higher values more. If you amplify the signal before applying tanh, the effect will be more pronounced.
Another alternative is a logarithmic transform. As the signal changes sign some pre-processing has to be performed.
If r is a series of sample values one approach could be something like this:
r.log1p <- log2(1.1 * (abs(r) + 1)) * sign(r)
That is, for every value take its absolute, add one, multiply with some small constant, take the log and then finally multiply it with the sign of its corresponding old value.
The effect can be something like this:
