I worked at an office that handled medical insurance claims, and we had fax machines. We would routinely exchange information with customers via fax. We upgraded to a fax server from our physical fax machines, and at the same time, to a voip solution. The fax trail went something like this:
Paper (analog) to PDF (digital) via a scanner sent to user's workstation.
PDF (digital) to fax server which places a FAX phone call using an analog audio modem signal (PSK).
VOIP inherently converts the analog signal to Digital, until it reaches the POTS, where it is converted back to analog.
Analog signal reaches the destination fax machine, where it is printed digitally.
With so many D/A and A/D conversions, we regularly had failed fax attempts due to line noise, quantization noise, etc.... It's amazing even a single fax ever got through. Many times, the customers just gave up.