Analog and Digital Technologies
Multiplexing

Multiplex combines several analog or digital signals and forwards the selected input into a single line, in telecommunication into telecommunication link. Multiplexers (or mux) are mainly used to increase the amount of data that can be sent over the network within a certain amount of time and bandwidth.

On the other hand, a demultiplexer (or demux) is a device taking a single input signal and selecting one of many data-output-lines, which is connected to the single input. A multiplexer is often used with a complementary demultiplexer on the receiving end.

## Frequency division multiplex

Frequency division multiplexing (FDM) is mainly an analog technology. Frequency division multiplex combines several digital signals into one medium by sending signals in several distinct frequency ranges over that medium.

Advantage of systems where channels are divided by frequency (a frequency multiplex) is that multiple signals belonging to multiple transmit sources and channels can be transmitted simultaneously. Another advantage is that signals can be transmitted via great distances.

On the other hand, disadvantage of frequency multiplex is channel interference, which is a result of using real (not ideal) filters, and both channel and electric circuits crosstalk.

Frequency multiplex works by assigning each signal mutually non-overlapping frequency bands ∆f1, ∆f2, ...., ∆fn. It is usually the case, that ∆f1 =∆f2 ... =∆fk = ∆fn. Of course, the frequency spectrum of transmitted signal has to fit the width provided by frequency band ∆fn.

Frequency spectrum for multiple channels

The frequency range of the transmission path F determines frequency boundaries of channels, e.g. minimum frequency of interval ∆f1 (∆f1min) and maximum frequency of interval ∆fn (∆fnmax).

A crucial part of frequency multiplex system on both the transmitter and receiver side is a band-pass filter. A band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. The bandwidth of the filter (∆fn) is simply the difference between the upper and lower cutoff frequencies. Selection of a proper band-pass filter depends mainly on the transmission speed.

Real band-pass filters do not have ideal characteristics and do not eliminate all frequencies above or below the cutoff frequency. Therefore a protective band ∆f0 must be in place. The ratio ∆ f0/∆f =kf depends on the amplitude-frequency characteristics of the band-pass filter in use (see image below) (more about filters in chapter Filters).

Amplitude frequency characteristic of ideal and real filter

The remaining question is, how do signals, which we want to transmit move to desired subband. It is via modulation on transmitter side and demodulation on receiver side. Each signal has a different carrier signal (see part about modulation in chapter Modulation), one that fits middle of the desired subband. It is later demodulated to its original form.

Frequency multiplex principle

Frequency multiplexing was mainly used in analog Telco systems, its current usage is mainly cable TV providers (each channel is on slightly different frequency – by switching a channel on a TV we tune to a different frequency band) and in optical communications.

## Time division multiplex

Time division multiplex (TDM) is used both in networking and phone systems and does exactly what the name says, e.g. takes samples from several slower speed signals, transmits it through one fast channel and restores the original signals.

The input device, also called multiplexer, selects one by one different source and takes a portion of its data and places it on the wire next. In this manner several "samplings" from several sources can be interleaved on the high-speed communications channel. This can be accomplished because the individual sources are sending their data at a relatively slow speed (i.e. 300 baud), while the outgoing channel has significant speed to accommodate a sampling from each source (i.e. 1200 baud). When the data reaches its transmit destination, another multiplexer disassembles the transmitted data and sends it to its destination, once again at the slower speed at which it entered the TDM system.

This technology is used by phone companies which have to put a large number of conversations over limited numbers of wires. If the conversations are broken up and put back together faster than human ear can detect, no one notices it. For this reason, high speed trunks use time-division multiplexing to carry several conversations at once.

One disadvantage of multiplexers that use time division multiplex is that they allocate a time slot even though the source is not sending any data or signal, which creates inefficiency.

Time division multiplex a) the first information b) the second information c) time slot multiplexing

### Synchronization

The synchronization of the sampling process is crucial at both ends of the channel. TDM devices must synchronize with one another so that the time moment required for each sampling matches. Otherwise, the demultiplexer would not be able to determine which source signal goes with what destination channel. Timing is therefore an extremely important element to a time-based methodology like TDM.

The time synchronization is based on transmitting a reference time impulses by a transmitter. The receiver must synchronize itself based on the received impulses. There is also frame synchronization – each frame has a special position, usually designating beginning of a frame with a special character.