# Bandwidth of telephone wire

Internet providers try to sell us the more and faster "fast internet" - 15Mb, 40Mb, 100Mb, and so on. But it's well known that the bandwidth the channel (in the most cases it's the telephone wire) restricted by the nature law. And this law is so fundamental as the light speed. (see, e.g., V.A.Kotetlnikov theorem). The bandwidth of a telephone wire is significantly less than providers propose us.

Can someone explain what is the matter here?

• Maybe ISPs are lying bastards? That's probably true, but at least around here I don't know of any ISP advertising 100Mb/s over telephone. Cable, yes. Telephone, no. – Phil Frost Aug 7 '14 at 20:30
• Sure. But what is the trick? – Yury Bendersky Aug 7 '14 at 20:31
• Trick to what, false advertising? Not much of a trick really, you just say things that aren't true. – Phil Frost Aug 7 '14 at 20:33
• Broader bandwidth means more expensive network equipment to keep the infrastructure working. There is also the impression of added value for higher speeds. So, many ISP's do provide the bandwidth advertised (as any simple speed test will show) - the reason there are so many different "speeds" available has more to do with logistics and economics than with physics proper. – Renan Aug 7 '14 at 21:14
• The new services (cable broadband and "U-Verse" in the US) don't use the phone network to send signals over long distances, so they're not limited by the bandwidth of phone lines. (U-Verse may use the phone network for the last 100 m or so, but bandwidth is inversely proportional to line length so the b/w of 100 m of telephone line is 10x that of 1,0000 m). – The Photon Aug 7 '14 at 21:22

The propagation speed and the symbol rate are completely different concepts. The symbol rate is the rate at which you can transmit information (hence 'symbols'), and it is closely related to the bandwidth, which is the span of frequencies which can propagate well through the wire. The relationship between the symbol rate and the bandwidth was recently explored in

Why is bandwidth, range of frequencies, important when sending wave signals, such as in radio?

and my answer there goes a long way towards answering your question. Symbol rates of 100Mbps correspond to bandwidths of about 200MHz, which are perfectly reasonable for appropriate wires. Whether your ISP is actually implementing the technology to match their advertising - that's another matter, but the technology is certainly available.

The "fundamental law" you refer to is the Whittaker–Nyquist–Kotelnikov–Shannon theorem, and it simply states that if you want to observe a signal of frequency ~$\nu$, you should sample at about twice that frequency (I suggest you study the theorem statement closely). This is not really a problem for telephony - it simply dictates the rate at which you need to sample the signal. This sampling rate is roughly equal to the symbol rate, or slightly bigger by a small overhead. Sampling at 100Mbps is not a problem for a modern device, since processor speeds of >1GHz, ten times bigger, are prefectly possible.

• Maybe relevant: Since cables carry electricity moving at the speed of light, why aren't computer networks much faster? But, I think the question wasn't about the speed of light -- it was just using that as an example of unbreakable physical laws. – Phil Frost Aug 7 '14 at 20:35
• Please don't complicate the question. If I want to have N bits per second at my side of channel and you are ready to give me N bit/sec you need give me a channel with bandwidth not less than N bit/sec. The propagation speed and the symbol rate are absolutely have no relevance to the question. Please be more attentive. – Yury Bendersky Aug 7 '14 at 21:10
• That is in the end up to you. If that is how you see it then I'm afraid the question is not at all clear. What exactly do you think is the limitation? Of course you will need a channel with an appropriate bandwidth, but those are perfectly available for the bandwidths in current commercial use. What makes you think they're not? – Emilio Pisanty Aug 7 '14 at 21:16
• A traditional phone line can transmit less than 100 kbit/sec and TV cable - less than 20 mbit/sec. This is a standard. – Yury Bendersky Aug 7 '14 at 21:22
• @YuryBendersky, you're more likely to get people to try to answer your question if you're not a jerk to the people who have already tried. Now downvoting your question so it won't keep getting floated to the front page. – The Photon Aug 8 '14 at 2:07