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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 DSB-SC 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
DSB-SC spectrum in Fig. 4.32b by suppressing the undesired sidebands using a proper 288 4 C ontinuous-Time Signal Analysis: T he Fourier Transform filter. For instance, the USB signal in Fig. 4.38a can be obtained by passing the DSB-SC
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 DSB-SC 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 frequency-domain, demodulation (multiplication by cos wet amounts to shifting the
LSB spectrum (Fig. 4.38b) to the left and the right by We (times one-half) 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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