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Unformatted text preview: odulation I n a mplitude m odulation, t he a mplitude A o f t he c arrier A cos (wet + l1e) is
varied in some m anner w ith t he b aseband ( message)t signal met) (known as t he
tThe term baseband is used to designate the band of frequencies of the signal delivered by the
source or the input transducer. 4 Continuous Time S ignal Analysis: T he F ourier Transform 4.7 m et) 278 T he r elationship o f B t o We is of interest. F igure 4.31c shows t hat We ?: 27l' B in
o rder t o avoid t he o verlap o f t he s pectra c entered a t ± we. I f We < 27l' B , t he s pectra
o verlap a nd t he i nformation o f m (t) is l ost in t he p rocess o f m odulation, a loss w hich,
m akes i t i mpossible t o g et b ack m (t) from t he m odulated s ignal m (t) cos w et.t (Modulated Signal) (Modulating Signal) (a) Modulator Application t o C ommunications: A mplitude M odulation 279 • E xample 4 .17
For a baseband signal m (t) = cos wmt, find the DSB signal, and sketch its spectrum.
Identify the upper and lower sidebands. M (w) m et) We shall work this problem in the frequencydomain as well as the timedomain
in order to clarify the basic concepts of DSBSC modulation. In the frequencydomain
approach, we work with the signal spectra. The spectrum of the baseband signal m (t) =
cos wmt is given by  M(w) = 7l'[6(w  wm ) + 6(w (b) + wm)] The spectrum consists of two impulses located a t ± wm , as depicted in Fig. 4.32a. The
DSBSC (modulated) spectrum, as indicated by Eq. (4.70), is t he baseband spectrum in
Fig. 4.32a shifted to the right and the left by We (times onehalf), as depicted in Fig. 4.32b.
This spectrum consists of impulses a t ±(we  Wm) and ±(we + Wm). T he spectrum beyond
We is the upper sideband (USB), a nd t he one below We is t he lower sideband (LSB). Observe
t hat t he DSBSC spectrum does not have the component of the carrier frequency We. This
is why it is called d ouble s idebandsuppressed c arrier ( DSBSC) .
M (m) (c) F ig. 4 .31 (a) DSBSC modulation. m odulating s ignal). T he f requency We a nd t he p hase (Je a re c onstant. W e c an assume (Je = 0 w ithout a loss of generality. I f t he c arrier a mplitude A is m ade d irectly
p roportional t o t he m odulating s ignal m (t), t he m odulated s ignal is m (t) cos wet
(Fig. 4.31a). As was i ndicated e arlier [Eq. (4.41)], this t ype o f m odulation s imply
shifts t he s pectrum o f m (t) t o t he c arrier frequency (Fig. 4.31c). T hus, i f m (t)
t hen m (t) cos wet < ===} < ===} 1
Z [M(w rrJ2
USB t t LSB  we)] (4.70) R ecall t hat M (w  we) is M (w) s hifted t o t he r ight by We a nd M (w + we) is M (w)
s hifted t o t he l eft b y We' T hus, t he p rocess o f m odulation s hifts t he s pectrum o f t he
m odulating s ignal t o t he left a nd t he r ight b y We' N ote also t hat i f t he b andwidth
o f m (t) is B Hz, t hen, as i ndicated i n Fig. 4.31c, t he b andwidth of t he m odulated
s ignal is 2 B Hz. We also observe t hat t he m odulated s ignal s pectrum c entered
a t We is c omposed o f two p arts: a p ortion t hat lies...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.
 Spring '13
 Bayliss
 Signal Processing, The Land

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