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The Modem (modulator-demodulator)

Operating at the Network and Data Link layers of the OSI model, ADSL modems are usually used to send and receive digital data over a phone line. When sending data, the modem modulates the data into analog signals that can be sent over the phone line. When receiving data, the modem demodulates the analog signal to digital data.
ADSL modems use different frequencies from those used to modulate voice over a phone line.

Because many ADSL modems also manage the connection and sharing of the ADSL service, a more accurate name would be 'ADSL modem/router'.

Continuing the journey...
 
After inspecting the packet, the modem's routing decision would be to transfer the packet to its default gateway; this would be a router at the ISP (Internet Service Provider).
Mostly, when using PPP over PPPoA (see the protocol stacks), the address resolution needed is to find the right ATM Virtual Circuit, but the ADSL connection between the modem and the DSLAM (to be explained later) is established when the modem is powered on and remains so until powering it off. Hence, the address resolution discovery happens only once during the lifetime of the link.
In the case of an Ethernet-based ADSL network, PPP over PPPoE (see the protocol stacks) is used. The modem creates a virtual Ethernet interface to encapsulate the IP packet with Ethernet framing. The address resolution needed here is the familiar ARP, and then the frames are encapsulated with ATM framing.
We shall note that in the ATM-based ADSL there are some ISPs that uses PPTP or L2TP to create a VPN with the subscriber.
At last the modem converts the digital data to analog data and sends it through the phone line.
Next stop: the splitter... click on the splitter icon

Network Components
Home or office computerTelephone
ADSL ModemSplitter
Voice SwitchSplitter
DSLAM
ATM or Ethernet Network
ISP
Internet