Communication Networks/Analog and Digital Telephony

Modems Introduction
'''The telephone network was originally designed to carry voice data. The human ear can only really hear sounds up to the 15 kHz range, and most of that is just high-frequency fluff noise that isn't needed to transmit human voice signals. Therefore, the decision was made to limit the telephone network to a maximum transmission frequency of 3400 Hz, and a minimum frequency of 400 Hz (to limit the passage of DC signals, which could damage the circuit). This gives the telephone network an effective bandwidth of 3000 Hz, which is perfect for transmitting voice, but which isn't that good for transmitting anything else.'''

'''Original telephone modems would use the existing telephone network to carry internet signals to a remote ISP. However, new DSP modems use a much larger frequency band, and this information is separated from the phone network almost as soon as it leaves your house. New voice technologies, such as VoIP completely bypass the old telephone infrastructure, and instead transmit voice signals over the internet.'''

The chapters in this section will talk about the analog and digital hybrid nature of the telephone network.

Modems
Modems were the original widespread method for home users to connect to the internet. Modems modulated digital data according to different schemes (that changed as time passed), and transmitted that data through the telephone network.

The telephone network was originally designed to only transmit voice data, so most of the network installed a series of low-pass filters on the different lines, to prevent high-frequency data or noise from damaging the circuits. Because of this, the entire telephone network can be seen as having a hard bandwidth of 3000 Hz. In reality, the lines used have a much higher bandwidth, but the telephone network cuts out all the high-frequency signals. DSL modems make use of that "lost bandwidth", but the original modems had to work within the 3000 Hz limit.

If we take the Shannon channel capacity of a telephone line (assuming a signal SNR of 40db, which is nearly impossible), we can get the following result:

$$C = 3000 \log_2 (1 + 10000) \approx 40 kbps$$

If we then plug this result into Nyquist's equation, we can find how many levels of transmission we need to use to get this bit rate:

$$r_b = 2W log_2(m)$$

which gives

$$m = 2^{\frac{r_b}{2W}} = 2^{\frac{40000}{6000}} = 2^6.67 < 2^7 = 128$$

Therefore, using a 128-level transmission scheme, we can achieve a theoretical maximum bit rate of 40kb/sec through a modem.

56k Modems
If the theoretical Shannon capacity of the telephone network is 40kbps, how can modern modems achieve a speed of 56kb/sec? The V.42 modem standard (which is what a 56k modem is) utilizes a standard implementation of the Lempel-Ziv compression algorithm, to shrink the size of transmitted data, and therefore apparently increase the transmission speed. The telephone companies aren't magically breaking the Shannon bound, they are just finding an interesting path around it.

DSL
A single strand of twisted-pair telephone wire has a bandwidth of nearly 100 kHz, especially over short distances. Over longer distances, noise will play a much bigger role in the received signal, and the wire itself will attenuate the signal more with greater distance. This is why DSL is only offered in locations that are close to the telephone office, and not in remote areas.

DSL signals require the addition of 2 new pieces of hardware: The DSL modem, and the DSL splitter, which is located at the telephone company, and splits the DSL signal (high frequencies) from the voice signal (low frequencies). Also, some houses may require the installation of additional filters, to prevent cross-talk between DSL and voice signals.

VoIP
With the advent of modems and DSL technology, telephone companies have become an integral part of the internet. It's no surprise then, when phone calls start getting digitized, and sent through the internet, instead of the old telephone network. Voice over IP (VoIP) is the logical conclusion to this train of thought.