The heartbeat is an effect with many (component) causes. There are electrical impulses, which cause movements of the heart muscle, which in turn cause blood and valves (and other parts of the heart?) to move; the sound from these movements travels through various kinds of tissue/cavities/etc. and ends up being received somewhere outside the body.
Where in this chain do the differences between one heartbeat and another originate? I'm assuming that things can go awry at any stage: irregularities in the nerve impulses, improper muscle response (for example: because the timing of the impulses is too fast for the muscles to respond), valves that are misformed, etc. So, there is (potentially, at least -- I don't know how this turns out in practice) a lot of information in the heartbeat. How can we tease out the contributions of the various components?
Here's a stylized picture of a heartbeat-like wave:
During the first half of the wave, the amount of energy increases up to a peak; in the second half, the amount of energy decreases back to zero; so, instead of plotting displacement/pressure (a) , we could plot energy (b):
Presumably, the energy increase in the wave happens because energy is being added by the heart muscles, and the energy decrease happens because of damping. So, we could also plot the amount of energy being added (c):
This perhaps corresponds to the intensity of the nerve impulses? I'm guessing. I don't know the technical name for the transform that takes us from (a) to (b) (in electronic music parlance, it's the "envelope"). From (b) to (c) is some kind of derivative. We could go a step further and take the derivative again (d):
All of these transformed views of the wave seem potentially useful. For example, here's a wave in which the amount of energy being added changes 1/4-way through, resulting in a change of frequency but the same displacement/pressure (higher frequencies at the same amplitude carry more energy):
The raw wave doesn't look that much different, nor does the envelope, but the derivative and the second derivative show the differences more clearly. So it might be useful to add these kinds of transforms to the heartbeat display.