What device connects a customer's equipment to a digital communication line in telecommunications?

The device that connects a customer's equipment to a digital communication line in telecommunications is a CSU/DSU, which stands for Channel Service Unit/Data Service Unit. This device serves a critical role in digital transmission systems, acting as a bridge between the digital signals from a customer's equipment, like a router or switch, and the digital circuit provided by a telecommunications carrier.

A CSU/DSU performs several essential functions. It is responsible for signal conditioning, managing line coding, and ensuring that the line’s electrical characteristics are within the specifications needed for proper signal transmission. Additionally, it establishes a connection to the digital circuit service provided by the telecommunications provider, facilitating a reliable data communication channel.

While a modem is designed to modulate and demodulate signals for analog lines, and a router directs data traffic between networks, they don't specifically connect to digital communication lines in the same way a CSU/DSU does. Similarly, a hub functions as a basic networking device that connects multiple Ethernet devices, but it does not interface with telecommunications lines directly. Hence, the CSU/DSU is the most accurate choice for this specific function in the context of telecommunications.