Phone companies impose this limited bandwidth so they can frequency multiplex long distance calls on a single line.
The bandwidth limit is acceptable because human speech is intelligible using this band of frequencies.
Shannon recognized that switches, at that time, and today’s logic circuits followed the rules of Boolean Algebra. Shannon’s Theory of Communications explains how much information you can send through a communications channel at a specified error rate.
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In another article I’ll discuss some of the smart coding techniques used to approach channel capacity.
If you can understand the mathematics, here is the first part of the paper as published in the Bell System Technical Journal in July 1948 and the remainder published later that year.
Shannon used a 3 decibel drop in signal strength to determine the limits.
A twisted pair has a larger bandwidth than 3000 Hz so they are not the reason for the narrow POTS bandwidth.
The bigger a pipe, the more can be pushed through it.
This statement holds true of all communication channels whether radio frequency (RF), fiber optic, or a POTS twisted pair of copper wires.
The bandwidth of a channel is the difference between the highest and lowest frequencies that will pass through the channel.