FDM and TDM with block diagrams

Multiplexing is the process of combining several independent message signals into one composite signal so that they can be sent over a single transmission medium; the reverse process at the receiver is demultiplexing. It saves cost because one high-capacity link replaces many separate links.

Frequency Division Multiplexing (FDM)

The available bandwidth is divided into frequency bands; each signal modulates its own carrier and occupies one band. All signals are sent at the same time.

 TRANSMITTER
 ch1 -[LPF]-[Mod f1]-[BPF]-+
 ch2 -[LPF]-[Mod f2]-[BPF]-+--(SUM)--> line
 chN -[LPF]-[Mod fN]-[BPF]-+

 RECEIVER
       +-[BPF f1]-[Demod f1]-[LPF]-> ch1
 line -+-[BPF f2]-[Demod f2]-[LPF]-> ch2
       +-[BPF fN]-[Demod fN]-[LPF]-> chN

Working:

1. Each baseband signal is band-limited by an LPF (voice 0.3–3.4 kHz).
2. It modulates a sub-carrier $f_1, f_2, \ldots, f_N$ (SSB-SC in telephony to save bandwidth).
3. A BPF keeps only the wanted sideband; channels are spaced 4 kHz apart, leaving guard bands.
4. All outputs are summed and transmitted.
5. At the receiver, BPFs separate each band, demodulators bring it back to baseband and LPFs recover each message.

Example: CCITT basic group – 12 voice channels in 60–108 kHz.

 amplitude
   |  [ch1]  [ch2]  [ch3]  [ch4]
   |  |   |g |   |g |   |g |   |
   +--+---+--+---+--+---+--+---+--> f
      f1     f2     f3     f4
 g = guard band

Time Division Multiplexing (TDM)

The time axis is divided into frames and each frame into time slots; each signal is sampled and sent in its own slot in turn, using the full bandwidth during that slot.

 ch1 -[LPF]-o                     o-[LPF]- ch1
 ch2 -[LPF]-o \                 / o-[LPF]- ch2
              (rotating)  link (rotating)
 chN -[LPF]-o / switch ------> \  o-[LPF]- chN
            commutator     decommutator
              ^                    ^
              +-- clock / sync ----+

Working:

1. Each signal is band-limited by an LPF.
2. A commutator (electronic rotating switch) samples channel 1, 2, …, N in turn at the sampling rate $f_s \geq 2f_m$ (8 kHz for voice).
3. The interleaved samples (PAM) are usually quantised and coded (PCM) and sent with frame synchronisation bits.
4. At the receiver a decommutator, synchronised to the transmitter by the clock and framing pattern, sends each sample to the correct output, where an LPF rebuilds the signal.

 |<-------------- one frame ------------->|
 | S1 | S2 | S3 | ... | SN | S1 | S2 | ...
  slot slot              slot
 S_i = time slot of channel i

Example: E1 – 32 slots × 8 bits × 8000 = 2.048 Mbps carrying 30 voice channels.