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Unformatted text preview: e 4 .20
Find the USB (the upper sideband) and LSB (the lower sideband) signals when
m et) = cos wmt. Sketch their spectra, and show t hat these SSB signals can be demodulated
using the synchronous demodulator in Fig. 4.33a.
The DSBSC signal for this case is <0 Jl (e) 01 Fig. 4 .37 Single sideband transmission. USB Spectrum 1 (4.79) As pointed out in Example 4.17, the terms ~ cos (we + wm)t and ~ cos (we  wm)t
represent the upper and lower sidebands, respectively. Figure 4.38a and b show the spectra <0 _ ( b) 1 0 1_ 1tI4 t
+ wm)t] r (a) LSB Spectrum ' PDsa.se(t) = met) cos wet i[cOS (We  Wm)t + cos (we (c) USB Spectrum <0 S ingle Sideband Modulation (SSB) = cos wmt cos wet
1 287 F ig. 4 .38 1 t (e)
: .1 0 1_ Single sideband spectra for m et) = cos wmt. of the upper and lower sidebands. Observe t hat these spectra can be obtained from the
DSBSC spectrum in Fig. 4.32b by suppressing the undesired sidebands using a proper 288 4 C ontinuousTime Signal Analysis: T he Fourier Transform filter. For instance, the USB signal in Fig. 4.38a can be obtained by passing the DSBSC
signal (Fig. 4.32b) through a highpass filter of cutoff frequency W e. Similarly, the LSB
signal in Fig. 4.38b can be obtained by passing the DSBSC signal through a lowpass filter
of cutoff frequency W e.
I f we apply the LSB signal ! cos (We  Wm)t to the synchronous demodulator in
fig. 4.33a, t he multiplier output is
1 e(t) = 2" cos (We  Wm)t cos wet = 1[cos wmt + cos (2we 4 wm)t] The term 1 cos (2we  Wm)t is suppressed by the lowpass filter, a fact which results in the
desired o utput 1 cos wmt (which is m (t)/4). The spectrum of this term is rr[6(w + WO) +
6(w  wo)]/4, as4depicted in Fig. 4.38c. In the same way we can show t hat the USB signal
can be demodulated by the synchronous demodulator.
In frequencydomain, demodulation (multiplication by cos wet amounts to shifting the
LSB spectrum (Fig. 4.38b) to the left and the right by We (times onehalf) and then suppressing the high frequency, as illustrated in Fig. 4.38c. The resulting spectrum represents
the desired signal ~m(t). • 4.8 Angle Modulat'ion 289 appreciably.:!: Thus, filtering of t he u nwanted sideband becomes relatively easy
for speech signals because we have a 600 Hz transition region around t he cutoff
frequency W e' For signals, which have considerable power a t low frequencies (around
W = 0 ), SSB t echniques cause considerable distortion. Such is t he case with video
signals. Consequently, for video signals, instead of SSB, we use another technique,
t he v estigial s ideband ( VSB), which is a compromise between SSB a nd DSB.
I t i nherits t he a dvantages o f SSB a nd DSB b ut avoids their disadvantages. VSB
signals are relatively easy t o generate, a nd t heir bandwidth is only slightly (typically
25%) greater t han t hat o f t he SSB signals. In VSB signals, instead of rejecting one
sideband completely (as in SSB), we a ccept a gradual cutoff off of one sideband 4 . 4 .8 Angle Modulation A sinu...
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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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