Multiplexing
Suppose two communicating stations connected to each other by data link and stations are not able to utilize the full capacity of data link, the data link can be shared for achieving this. Multiplexing is the technique by which simultaneous transmission of multiple signals through data link is possible. A generic term for such sharing is multiplexing.
For example, in Figure the communication stations on the left direct their transmission streams to a multiplexer (MUX), which combines them into a single stream. At the receiving end that stream is fed into a demultiplexer (DEMUX), which separates the stream back into its component transmissions and directs them to their intended receiving communication stations.

 Frequency Division Multiplexing (FDM)
Frequency division multiplexing is used with analog signals. Perhaps its most common use is in television and radio transmission. A multiplexer accepts analog signals from multiple sources, each of which has a specified bandwidth. The signals are then combined into another, more complex signal with a much larger bandwidth. The resulting signal is transmitted over some medium to its destination where another MUX extracts and separates the individual components. Carrier frequencies are separated by enough bandwidth to accommodate the modulated signal. These bandwidth ranges are the channels through which the various signals travel.
Figur illustrates FDM. The transmission path is divided into three parts, each representing a channel to carry one transmission. Here division of channel is based on frequency.

For example, imagine a point where three narrow streets merge to form a three­ lane highway. Each of the three streets corresponds to a lane of the highway. Each car merging onto the highway from one of the streets still has its own lane and can travel without interfering with cars in the other lanes.
  Time Division Multiplexing (TDM)
In time division multiplexing (TDM) many input signals are combined and transmitted together, as with FDM. TDM is used with digital signals. Multiple transmissions can occupy a single link for specific time. Each source of transmission is authorized to use the link for a specific period. Figure 2.33 illustrates TDM.       

In the figure portions of signals 1, 2 and 3 occupy the link sequentially.
Two basic forms of TDM are in use today: synchronous TDM (STDM) and asynchronous TDM (ATDM).
In synchronous TDM, the multiplexer allocates exactly the same time slot to each transmission device at all times, whether or not a device has anything to transmit. Time slots are grouped into frames. A frame consists of one complete cycle of time slots, including one or more slots dedicated to each transmission device. In a system with n input lines, each frame has least n slots, with each slot allocated to carrying data from specific input line. If all the input devices share a link and transmit at the same data rate, each device has one time slot per frame.

Only a portion of the time slots is in use at a given instant, in synchronous TDM, because the time slots are pre-assigned and fixed. Whenever a connected device is not transmitting, the corresponding slot is empty and much of the path is wasted.
Asynchronous time division multiplexing or statistical time division multiplexing, is designed to avoid this type of waste. The number of time slots is an asynchronous TDM frame, m, which is based on a statistical analysis of the number of input lines that are likely to be transmitting at any given point. Rather than being pre-assigned, each slot is available to any of the attached input lines that has data to send. Multiplexer scans the input lines, accepts portions of data until a frame is filled, and then sends the frame across the link. If there are not sufficient data to fill all the slots in a frame, partially filled frames are transmitted, thus full-link capacity may not be used 100 per cent of the time. This reduces wastage of path.

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