What kind of device converts signals from a campus's analog phone equipment into ip data that can travel over a phone company's analog telephone lines?

I’d go with an ATA (Analog Telephone)

ATA converts analog voice signals to digital signals, which can be transmitted over the internet. This device lets you connect a standard telephone to a network so that it can use VOIP to make calls through the user’s internet connection. Without this device, there will be no connection between the analogue telephone and a digital network.