0195136047.pdf

646 SIGNAL PROCESSING

x(t)

(a)

(b)

x(t)

t

PA M

t

0 Ts 2 Ts 3 Ts 4 Ts 5 Ts

Ts 2 Ts 3 Ts 4 Ts 5 Ts

0

PDM

t

0

PPM

t

0

Low-pass

filter

Pulse

generator

Transmission

medium

Pulse

converter

Low-pass

filter

Figure 14.2.7(a)Typical pulse modulation system.(b)Waveforms.

aspulse amplitude modulation(PAM),pulse duration modulationorpulse width modula-

tion(PDM or PWM), andpulse position modulation(PPM), respectively. At the output end,

the modulated pulses are converted back to sample values for reconstruction by low-pass

filtering.

EXAMPLE 14.2.1

In order to demonstrate aliasing, make a plot of the signal

x(t)=3 cos 2π 10 t−cos 2π 30 t

which approximates a square wave withW=30 Hz. If the sample points are taken at

t= 0 ,

1

60

,

2

60

, ...,

6

60

corresponding toTs= 1 /( 2 W), you can see thatx(t) could be recovered from those samples.

However, if the sample points are taken at