How well can digital phone lines carry dial-up connections? It was an issue in the early days of digital lines - same as with fax. For fax we got v.34 and other improvements. IDK about dialup tho.
If you can run g.711 for your codec, things should work ok, depending on your jitter... g.711 is the digital calling code from 1972 that telcos used for T1/E1. On voip, it's packetized into 20ms bursts rather than multiplexed one sample at a time.
If you use one of the newer predictive voice codecs, expect a lot less success, but maybe moving to older/slower modem speeds will help.
Early digital lines were purely circuit switched and didn’t add any jitter (unlike modern VoIP based “lines”), so there shouldn’t have been any problems running analog or digital fax over these.
V.34 was mostly a speed improvement, as far as I remember, no?
I think WarOnPrivacy was thinking of the T.38 standard. Once T.38 gained enough adoption in the various providers fax over IP became far more reliable.
edit: That is I assume that they meant VoIP when they say digital phone lines. Fax over digital ISDN lines has been reliable since its inception as far as I am aware.
If you have an ATA like a Cisco SPA122 , Linksys or Polycom 302, then you should be able to get between 2400 and 14,400 baud speeds; you will have to try different speeds.
Faxes routinely get 9600 and 14,400 speeds over these ATAs; it helps a great deal if your coded is G711 which is an uncompressed codec (it is u-law PCM in the USA; PCM is just like the bits recorded on a music CD, but at a much lower bitrate).