It’s helpful here to understand that there are two things involved with digital sampling: Of foremost importance is the sampling; secondarily, subsequent digitization allows us a number of conveniences.
That is, sampling theory does not require digitizing—you can store the analog levels obtained by sampling a signal whose spectrum is below half the sample rate. Play it back by running the samples as analog impulses, at the original sample rate, through a lowpass “reconstruction” filter set just below half the sample rate. You can even perform signal processing on the analog samples before the reconstruction filter, such as an analog multiplier to control gain.
If you’ve even seen or used an analog delay guitar pedal, that’s how it works. But you also might know that fidelity is not great, because it’s not easy to retain the analog values without degradation, resulting in noise and loss of high frequencies. And more advance signal processing in the analog domain can be costly and difficult to implement.
But if we digitize those samples, we are assured that they retain their values without change for an indefinite amount of time. And if we store them in a numerical processor, we can use many advanced digital signal processing techniques on them, limited only by the processor speed.
One of the few concessions we must make is that we need to decide on the digital precision we use to obtain and store the digitized values. Fortunately, we’ve been able to get very good precision, affordably. Limits of the human ear and electronics (thermal noise is unavoidable above absolutely zero) run around 20 bits, and we usually support 24 bits mostly because it’s an even byte above the minimum we accept as high-quality (16-bits), and allows for additional headroom.
So, sampling is what you referred to as the X-axis, the time axis. Here you’re mainly talking about long-term clock accuracy and jitter, both of which we’re very good at. We rarely have to worry about this, and it’s not something that normal signal processing algorithms can affect. So while sample rate is an important consideration for bandwidth, maintaining it is not an issue.
And the Y-axis is essentially the digitization accuracy. We’re also very good at that, but in our digital signal processing algorithms we need to take care that we aren’t degrading the level we already have, by neglecting quantization effects that can grow with poorly designed algorithms. Quantization effects are one of the major points that DSP coders need to pay attention to.