M Quack said:
The relevant equation in the video is: [itex]\Delta f \cdot \Delta t \approx 1[/itex]
To transmit a bit you need a pulse of length (in time) [itex]\Delta t[/itex] that is either on or off.
The data rate then is about [itex]1/\Delta t[/itex], so the maximum data rate in bit/second is about the same as the band width [itex]\Delta f[/itex] in Hertz.
For a real, working transmission line you need a bit of overhead for synchronization etc. so the practical data rate will be lower than this limit.
See also the Shannon Hartley theorem that takes signal/noise ratio into account.
http://en.wikipedia.org/wiki/Shannon–Hartley_theorem
That is an incredible underestimate of the information capacity of a transmission system. It assumes that you are sending rectangular (top hat) shaped pulses, which is something that no telecoms system would involve.
To understand what information is being carried in a 'digital' channel, you need to accept that the signal being carried will be in the form of a variation of an
analogue quantity. (e.g. a varying voltage, current, light intensity etc. etc). The actual 'information' in a noise free time varying signal, at any time, is not what would be its binary value but its analogue value - to as many significant figures as you care to use (a lot of - potentially infinite - information).
All digital channels pass through a low (or band) pass filter, which spreads each pulse out in time. This will produce inter-symbol interference where the analogue value of each symbol (bit etc) affects the analogue value of those near it in time. If you display a typical binary signal, filtered to fit a particular channel bandwidth, on a correctly synced oscilloscope, you get an 'eye pattern' (
See this link and many others). As long as you sample the incoming signal at the centres of the eye pattern, you can get 'the right answer' and reconstitute your original digital data. (Yes - there may be an overhead involved, to deal with the need to synchronise your decoder, but a long enough delay can take care of that, however bad the timing is.
In the end, the bandwidth can be reduced and reduced until the noise in the channel is enough to 'close' the eye and the channel will fail. The original Shannon paper derives this from absolute scratch - basing everything on using Morse Code (iirc) and derives the Shannon Hartley equation. This says that
the only limit to data rate in a given bandwidth is, in fact, the Signal to Noise Ratio. No system has been made to work very close to this limit but modern systems, using modulation methods that are matched to the nature of the likely noise characteristic of a channel, do a very good job. If errors are detected and corrected, the overhead for the extra data can well produce stunning figures for the useful channel capacity. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-451-principles-of-digital-communication-ii-spring-2005/lecture-notes/chap4.pdf describes methods whereby the Shannon link can be approached. (If the theory is not familiar, it can be a bit demanding as its not intuitive).