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Consider a case where i’m listening to a recorded audio on internet.Basically the useful audio Frequency range lies b/w 40hz to 4khz, which has a BW of 4khz which is pretty low ,does that mean the audio has low data rate? But it loads up pretty quickly.

Another question:- does higher message signal BW mean it can accomadate MORE info at a time and lead to fater data rates, as more data is being transferred per second?

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The concept you are searching for is called channel capacity. If you do a web search on that term you should find a lot of information.

Basically, the capacity of a channel is determined by it's bandwidth, noise level, and the power you can put into your signal. Theoretically, if I could only send one symbol per second I could still achieve 1Mbps as long as the noise was low enough to distinguish gradiations in the signal of \$10^{-6}\$. OTOH, a 1MHz wide channel with so much noise that I could only send binary signals could also achieve that speed.

The "truth" is always somewhere in the middle, and provides a continual challenge for communications engineers to get more speed for less money on existing channels.

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The data throughput for a channel is defined by two things:

  • Signal bandwidth
  • Signal-to-noise ratio

This is expressed in the Shannon Information Theorem. That is:

$$C = W *log_2(1 + SNR)$$ Where W represents the bandwidth and C is the capacity of the channel.

Mind, this is the information capacity for data that has infinite entropy, that is, the data is truly random and thus isn't compressible by any means.

More about the Shannon Information Theorem here: http://www.inf.fu-berlin.de/lehre/WS01/19548-U/shannon.html

And, C. E. Shannon's actual paper: http://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf

If we employ compression, the throughput can be increased substantially. This can range from about 2:1 for a simple scheme like G.711 mu-law to much higher using transform+entropy based codecs like MP3 and others.

A comparison of compression formats here: http://www.sericyb.com.au/audio.html

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