Case studies for CT systems - Continuous and Discrete Time Signals and Systems - page 371

C ( w )

M ( w )
1

p

w w

− w max

w max − w c w c

(a) (b)

S ( w )
p
0.5 k

Fig. 8.3. Amplitude modulation
in the frequency domain.
(a) Spectrum of the baseband
information signal.
(b) Spectrum of the carrier
signal. (c) Spectrum of the
modulated signal.

w

− w c

w c

(c)

We now consider the extraction of the information signal x ( t ) from the mod-
ulated signal s ( t ). This procedure is referred to as demodulation, which is
explained in Sections 8.1.1 and 8.1.2.

8.1.1 Synchronous demodulation

The objective of demodulation is to reconstruct m ( t ) from s ( t ). Analyzing the
spectrum S ( ω ) of the modulated signal s ( t ), the following method extracts the
information-bearing signal m ( t ) from s ( t ).

(1) Frequency shift the modulated signal s ( t )by ω c (or −ω c ). If the modulated
signal is frequency-shifted by ω c , one of the side bands is shifted to zero
frequency, while the second side band is shifted to 2 ω c . Conversely, if
the modulated signal is frequency-shifted by −ω c , the two side bands are
shifted to zero and − 2 ω c .
(2) In order to remove the side band shifted to the non-zero frequency, the
result obtained in Step (1) is passed through a lowpass filter having a pass
band of ( −ω max

≤ ω ≤ ω max ). The output of the lowpass filter consists
of a scaled version of the modulating signal and an impulse at ω = 0.
The impulse represents the dc component and is removed by subtracting a
constant value in the time domain as shown in Step (3).
(3) A constant voltage equal to the dc component is subtracted from the output
of the lowpass signal.

Step (1) can be performed by multiplying the AM signal s ( t ) by the demodulat-
ing carrier cos( ω c t ) having the same fundamental frequency and phase as the