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A multiplexor makes it possible for several devices to share a single communication line. Every device has a point to point connection to a device on the remote multiplexor, while there is just a single link available.
The way the main link is shared is three folded:

Multiplexors do not have any intelligence about the data they are multiplexing. They are interface dependend. The input ports are usually called channels and the output port is called the composite or main port.

Frequency Division Multiplexing:
FDMs devide the available bandwidth (Hz) of a link into multiple sub-channels with a smaller bandwidth. A good example is the way cable TV (CATV) is broadcasted to every home. A single cable contains all the channels you can choose from on your TV-set.
Guardbands are used to separate the sub-channels. This means there is some overhead. This kind of multiplexing isn't used often (meaning in a wide range of applications), because FDMs can be as easilly expanded as the other multiplexing technics.

Time Division Multiplexing:
TDMs use the full bandwidth for every channel, but not at the same time. In a round robin fashion every channel gets its time slice (time slot) to the shared link.
Each channel is sampled for a certain amount of time (the sample time depends on the number of channels and the input speed, length of a bit). The state of the channel is then send to the remote TDM where it is demultiplexed from the incoming bitstream and send to the corresponding channel. Because the sampling rate is a multiple of the bit time every bit is sampled more than once to prevent data loss. The aggregate rate of the channels can not exceed the rate of the composite port.
When channels are not used, their bandwidth is still reserved (an empty slot is send). A more efficient way of multiplexing is statistical multiplexing.

Statistical Multiplexing:
A STM tries to use the capacity of the line as optimal as possible. Every channel is buffered and only those channels that have something to send are multiplexed and send to the remote side. This requires some intelligence from the muxes and a way of indicating which data came from which port.
A large amount of data or many 'used' ports will soon flood the mux or the shared link.