Here's the technical description, from NSA.[1]

It was really an awful kludge. Today, you'd think, digitize audio into a bit stream, encrypt bitstream. That's not how it worked. It was somewhat similar to the older A-3 analog scrambler, which split up audio into a number of bands and rearranged them, changing the rearrangement occasionally. In SIGSALY, incoming audio was filtered out into 10 frequency bands. There was also a dominant pitch detector and a "hiss" detector for unvoiced content. That created 12 analog signals to encrypt. Those signals were much lower bandwidth than the original speech. The patent seems to indicate that the frequency band signals were merely encoded as above or below a threshold. Not a full A/D, just a 1-bit threshold. As late as 1973, people were still trying vocoder-like technologies, but it became easier to work on audio in the digital domain and that died out.[2]

The keying system changed the key every 20ms. It's not clear from the description whether the digitization of the 12 signals was also one sample for 20ms, but it probably was. If you used the same key bits for more than one analog sample, that would create a vulnerability. It's a one time key system, and those only work against serious opposition if the key is only used once. See VENONA.

The articles indicate that synchronizing the key stream, which was on phonograph records, was a huge synchronization headache. Keeping signals in sync was really hard, and was part of the curse of analog TV, with horizontal and vertical hold controls.

What this looks like is a system which had to work regardless of cost. So it was put together out of known building blocks. Straight digitization of audio was probably considered, especially since Alec Reeves, who had demoed pulse code modulation in 1937, was involved. But it was a high-risk technology. They would have had to invent a good A/D converter and a decent modem, which would have added technical risk to the project.

It's one of those systems of historical interest because it was too soon. You couldn't really do the job in the straightforward way, but it needed to be done, resulting in a magnificent kludge.

[1] https://www.nsa.gov/portals/75/documents/about/cryptologic-h...

[2] https://www.youtube.com/watch?v=UfpUexWJqb4

SIGSALY: Churchill's top secret hotline to the president