What Does a 3kHz Bandwidth Mean for a Leased Telephone Line?

[frenzal_dude]

What does it mean if a leased telephone line has a bandwidth of 3kHz?

Does it mean any signals traveling alone that line must have frequency components less than or equal to 3kHz?
Or does it mean that all the signals' frequency components (assuming time multiplexed) must add up to be less than 3kHz?

Also is bandwidth just the range of frequencies? So if a signal had frequencies from 1kHz to 3kHz, its bandwidth would be 2kHz?
Because in my signal theory classes they seem to use "highest frequency" and "bandwidth" interchangeably. For example some say the nyquist sampling rate is "twice the bandwidth", while others say it's "twice the highest frequency", but technically it should be twice the highest frequency right?

 

[MATLABdude]

Are you familiar with Fourier series on continuous signals? Basically, you can break down any arbitrary continuous signal into the sum of sinusoids of different frequencies:
http://en.wikipedia.org/wiki/Fourier_series

In the context of telephones, what this means is that the frequency components of your speech which are above 3 kHz gets removed, and the person listening to you hears only the lower frequency components. As the majority of human speech is in this range, you don't end up losing too much (although it is noticeable as compared to, say, real life or a cassette or CD recording:
http://en.wikipedia.org/wiki/Voice_frequency

Bandwidth means different things to different people, in different settings:
http://en.wikipedia.org/wiki/Bandwidth_(signal_processing)

The Nyquist frequency REQUIRED TO REPRODUCE A SIGNAL would be twice the highest frequency component of that signal. I believe that in this context (and I'm not a signals expert) that the bandwidth is being treated as the baseband (i.e. from near 0 to whatever the highest frequency happens to be).

 

[skeptic2]

What does it mean if a leased telephone line has a bandwidth of 3kHz?

Does it mean any signals traveling alone that line must have frequency components less than or equal to 3kHz?

No.

Or does it mean that all the signals' frequency components (assuming time multiplexed) must add up to be less than 3kHz?

It means that the difference between the upper -3 dB rolloff point and the lower -3 dB rolloff point is 3 kHz. The frequency response of a standard telephone circuit is from 300 Hz to 3300 Hz. (Sometimes given as 3400 Hz)

Also is bandwidth just the range of frequencies? So if a signal had frequencies from 1kHz to 3kHz, its bandwidth would be 2kHz?

Yes

Because in my signal theory classes they seem to use "highest frequency" and "bandwidth" interchangeably. For example some say the nyquist sampling rate is "twice the bandwidth", while others say it's "twice the highest frequency", but technically it should be twice the highest frequency right?

Your signal theory may be talking about signals being limited by a low pass filter or they may be trying to simplify the discussion. If you wanted to digitize a phone circuit as it is, yes you would need to sample it at a minimum of 6600 Hz. However if you were to mix that band with a 300 Hz oscillator, the difference frequency could be digitized at a 6000 Hz sampling rate. Radio channels are not sampled at the radio frequency but are mixed to a lower frequency, many times to baseband, meaning it's mixed down so that the lower side of the channel is at zero Hz in order to maximize the sampling rate vs. bandwidth.