Few fax machines have inbuilt T38 to get the best of it use T38 pass-through to an ATA that does, the end connection to the fax machine will be G711,
Again, to get better and less complicated fax communication look into spandsp, hylafax and T38modem/iaxmodem as appropriate, I use both, depending . . . ., failed faxes will be re-queued and only the remaining pages will be re-sent, We do thousands of pages a week by that method, some have dozens, even hundreds of pages, complete with fax2email and email2fax , it is not limited to pdf's either , you can send docx and even mac stuff through libreoffice to hylafax. We rarely have to apologize to the client 