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From the WiKi:

Modem (modulator–demodulator) is a network hardware device that modulates one or more carrier wave signals to encode digital information for transmission and demodulates signals to decode the transmitted information. The goal is to produce a signal that can be transmitted easily and decoded to reproduce the original digital data. Modems can be used with any means of transmitting analog signals, from light-emitting diodes to radio. A common type of modem is one that turns the digital data of a computer into modulated electrical signal for transmission over telephone lines and demodulated by another modem at the receiver side to recover the digital data.

From snapshot, is the twisted-pair line transfer digital data and ADSL line transfer the modulated electrical signal?

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To answer your question, "yes".

In your image, the twisted pair connection is Ethernet, carrying digital information in the form of a square wave.

To be able to transmit this on a telephone circuit (ADSL) which is designed for analog transmission, the square wave needs to be modulated into an analog signal that is compatible with the phone line. The analog signals are above the human hearing range, but usually a DSL splitter is installed to pass the low frequencies to telephone equipment and to prevent interference with the higher frequencies, such as reflections and ringing (not phone ringing, but more like signals bouncing back and forth).

You can read more about modulation at Wikipedia.

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    The telephone/ADSL line also uses twisted pair. Both use modulation to put digital data onto an analog medium albeit very different methods. The splitter is (was) required to protect legacy POTS hardware, not your hearing. – Zac67 Sep 30 '18 at 8:28
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ADSL is a set of standards for modulating digital data onto voice-grade twisted-pair cabling.

Ethernet (what you just call "twisted pair") modulates digital data onto data-grade twisted-pair cabling (category 5 or better). Ethernet also defines framing and addressing to connect a local network together.

Both use copper cabling and electrical signaling but they are quite different.

  • Are all twisted pair and ADSL transfer modulated electrical signal? – qg_java_17137 Sep 30 '18 at 4:06
  • Actually Ethernet was around before Category 5 cable. 10Mbit was possible on AUI, coax and Cat3.and using Cat3, you could go to 100Mbit using 100BaseVG equipment. Digital signals (1s and 0s) are modulated into discrete pulses of energy onto the Ethernet cable. zaielacademic.net/networking/signal_characteristics.htm – Dacid Salin Sep 30 '18 at 6:03
  • @DacidSalin The question was about twisted pair and 10BASE-T is (mostly) obsolete - I wanted to keep the answer simple. The "discrete pulses" aren't really there with 100BASE-TX onwards. – Zac67 Sep 30 '18 at 8:14

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