0195136047.pdf

14.2 MODULATION, SAMPLING, AND MULTIPLEXING 647

t= 0 ,

1

40

,

2

40

, ...

corresponding toTs= 1 /( 2 W)andfs< 2 W, a smooth curve drawn through these points will

show the effect of aliasing.

Solution

The waveforms are sketched in Figure E14.2.1.

x(t) Aliased waveform

t

0

− 2

2

1

60

1

40

3

= 40

3

60

2

40 =

6

60

4

40

2

60

4

60

5

60

Figure E14.2.1

Multiplexing Systems

A multiplexing system is one in which two or more signals are transmitted jointly over the
same transmission channel. There are two commonly used methods for signal multiplexing.
Infrequency-division multiplexing(FDM), various signals are translated to nonoverlapping
frequency bands. The signals are demultiplexed for individual recovery by bandpass filtering
at the destination. FDM may be used with either analog or discrete signal transmission.Time-
division multiplexing(TDM), on the other hand, makes use of the fact that a sampled signal is
off most of the time and the intervals between samples are available for the insertion of samples
from other signals. TDM is usually employed in the transmission of discrete information. Let us
now describe basic FDM and TDM systems.
Figure 14.2.8(a) shows a simple FDM system which is used in telephone communication
systems. Each input is passed through a low-pass filter (LPF) so that all frequency components
above 3 kHz are eliminated. It is then modulated onto individualsubcarrierswith 4-kHz spacing.
While all subcarriers are synthesized from a master oscillator, the modulation is achieved with
single sideband (SSB). The multiplexed signal, with a typical spectrum as shown in Figure
14.2.8(b), is formed by summing the SSB signals and a 60-kHzpilot carrier. The bandpass filters
(BPFs) at the destination separate each SSB signal for product demodulation. Synchronization is
achieved by obtaining the local oscillator waveforms from the pilot carrier. Telephone signals are
often multiplexed in this fashion.
A basic TDM system is illustrated in Figure 14.2.9(a). Let us assume for simplicity that all
three input signals have equal bandwidthsW.Acommutatoror an electronic switch subsequently
obtains a sample from each input everyTsseconds, thereby producing a multiplexed waveform
with interleaved samples, as shown in Figure 14.2.9(b). Another synchronized commutator at the
destination isolates and distributes the samples to a bank of low-pass filters (LPFs) for individual
signal reconstruction. More sophisticated TDM systems are available in which the sampled values
are converted to pulse modulation prior to multiplexing and carrier modulation is included after