The 1940s sigsaly secure voice communication model of PAM is nicely summarized by Forney at the chapter from his MIT courseware:
Its worth a read since it leverages the math that I, for one, have got down from studying quantum mechanics. Its more engineering than science, focussing on particular wave functions: sincT(). These get us to actual pulses, where in time periods values can be assured to be from an orthonormal set. One gets quickly to auto-correlation measures (which takes one quickly on to sensitive areas (still!) of crypto applied to satellite waveforms). Forney was more concerned with teaching sampling, indicating first from shannons rules about maximum spectral efficiency (given SNR, basically) one can build a random process model in continuous math then prove that an orthonormal expansion can represent the points without loss of information. Having managed to turn Hz carriers and power issues into a set of symbols being delivered at a particular rate due to the modulation, he then shows how coding can, optionally, further improve the performance.
Is fun then to turn from 1940s thinking, long tied to Lincoln and MIT, and onto Baez:
We get a view into some modern noise-related research topic founded in another 1940s topic: weiner processes.