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Unformatted text preview: a signal bandlimited t o B Hz (Fig. P4.7-2a). F igure
P4.7-2b s hows a DSB-SC m odulator available in t he stock room. T he b andpass filter
is t uned t o W e. T he c arrier generator available generates not cos wet, b ut cos wet.
( a) E xplain w hether you would be able t o g enerate t he desired signal using only this
equipment. I f so, what is t he value of k?
( b) D etermine t he signal s pectra a t p oints b and c, a nd i ndicate t he frequency bands
occupied b y t hese spectra.
( c) W hat i s t he m inimum usable value of We?
( d) Would t his scheme work if t he c arrier generator o utput were cos wet? Explain.
( e) Would t his scheme work if t he c arrier generator o utput were cos wet for any
integer n ?: 2? F ig. P 4.7-5
4 .7-4 F i?ure P4.7-4 p resents a scheme for coherent (synchronous) demodulation. Show t hat
thiS scheme can demodulate t he AM signal [A + m (t)] cos wet regardless of t he value
of A. 4.7-5 ~ket~h t he A M signal [ A+m(t)] cos wet for t he p eriodic triangle signal m (t) i llustrated
m Fig. P4.7-5 c orresponding t o t he m odulation index: ( a) J1. = 0.5, ( b) J1. = 1, ( c)
J1. = 2, a nd ( d) J1. = 0 0. How do you i nterpret t he case J1. = oo? 318 4 .7-6 4 C ontinuous-Time S ignal Analysis: T he F ourier T ransform For each of the following three baseband signals ( a) m (t) = cos lOOt ( b) m (t) =
cos lOOt + 2 cos 300t ( c) m (t) = cos lOOt cos 500t
(i) Sketch t he s pectrum of m (t).
( ii) Find a nd sketch the spectrum of the DSB-SC signal 2 m(t) cos 1000t.
( iii) From t he s pectrum obtained in (ii), suppress the LSB s pectrum to obtain the
USB s pectrum.
( iv) Knowing the USB spectrum in (ii), write the expression 'PUSB (t) for the USB
(v) Repeat (iii) and (iv) to obtain the LSB signal 'PLSB (t). Sampling F ig. P 4.8-1
4 .8-1 Sketch 'PFM (t) a nd 'PPM (t) for t he modulating signal m (t) depicted in Fig. P4.8-l,
given We = 2". X 107 , k f = 2". X 105 , and kp = 50".. A c ontinuous-time s ignal c an b e p rocessed b y p rocessing i ts s amples t hrough
a d iscrete-time s ystem. F or t his p urpose, i t is i mportant t o m aintain t he s ignal
s ampling r ate s ufficiently high so t hat t he o riginal signal c an b e r econstructed f rom
t hese s amples w ithout e rror ( or w ith a n e rror w ithin a given t olerance). T he necessary q uantitative f ramework for t his p urpose is provided by t he s ampling t heorem
d erived i n t he following section. 5.1 The Sampling Theorem F ig. P 4.8-2
4 .8-2 A baseband signal m (t) is a periodic saw tooth signal shown in Fig. P4.8-2. Sketch
'PFM(t) a nd 'PPM(t) for this m (t) if We = 2". X 106 , k f = 20,000"., and k p = "./2.
Explain w hy i t is necessary to use kp < ". in this case. 4 .8-3 For a modulating signal
m (t) = 2 cos lOOt + 18 cos 2000".t
Determine the bandwidths of the corresponding 'PFM (t) and 'PPM (t) if k f
a nd k p = l . We now show t hat a r eal signal whose s pectrum is b andlimited t o B Hz
Iwi > 2".BJ c an b e r econstructed e...
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