If in addition a carrier component is transmitted

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Unformatted text preview: ) cos(ωc t)] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 t/T 8 9 10 11 12 13 14 15 16 17 18 19 20 t/T 8 9 10 11 12 13 14 15 16 17 18 19 20 t/T USB: LPF[s(t) cos(ωc t)] 0 1 2 3 4 5 6 7 LSB: LPF[s(t) cos(ωc t)] 0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 t/T relaxed if we allow a part (“vestige”) of the unneeded sideband to be transmitted. If, in addition, a carrier component is transmitted, demodulation is simplified significantly. This vestigial sideband scheme is used for all commercial television transmissions, wherein the upper sideband and a vestige of the lower sideband are transmitted. Vestigial sideband is used for transmission of the video portion of analog television signals using the National Television Systems Committee (NTSC) system (see Figure 1.26a) and for transmittion of fr /2 = 5.381119 MHz 1 1 √ 2 Carrier 309.441 kHz 309.441 kHz 6.0 MHz Figure 1.26: The spectrum of a television signal as transmitted for digital television (DTV) using the ATSC (Advanced Television Systems Committee) 8VSB system. digital television (DTV) signals using the Advanced Television Systems Committee (ATSC) standard (Figure 1.26b). The ATSC modulation is called 8VSB. ATSC message signals are constructed using pulses whose Fourier transform is the square-root of the raised-cosine pulses discussed earlier. In the receiver, the signal is filtered using a square-root raised-cosine response so that the received pulses will have a wrThes iasefolaowan be found in an integral table or table of Fourier transforms and itt i n nt gr l l c s: the result is ∞ S (ω∞ = ) S (ω ) = π Ac s(t)e−j ωt dt (1.48) Jn (β )−(ω − ωc − nωm ) + Jn (β )δ (ω + ωc + nωm ) δ∞ 1.6. ANGLE MODULATION (NONLINEAR MODULATION) n=−∞ ∞ 35 (1.50) − =he Aicgnal set)j ωt s oa (spectrum swhωcht)dt sists of a se(1.49) This result shows that t s ( hac s ωc t + β in i m con t of −∞ 1s impul.es that are lo cated at the discrete frequencies ω = ±(ωc ± nωm ). The specThiruintconsilstcaof an ifnfinide inuan entegsialebands ohataarle sof araueierroransfe rms ier d t s m egra s n be oun t n mb ir of r d table t r t b e ep Fo trd f t m th o carr an 0u therres.elncis by integer multiples of the frequency of the modulating tone, ωm . The f equ 8t y mo dulation index ∞ is just a constant that describes the peak phase deviation of β 0.6 ( g ) = The theSsiωnal. π Ac functiJn(Jn δxω i− call− nthm ) +ssel (fu)δctio+ ofc firsnωm ) of o(1.50) on β )( ( ) s ωc ed ω e Be Jn β n (ω n ω + t kind rder n=−ar n. 0.4ese functions ∞ e tabulated, and for a given value of n, tables of Jn (x) can Th be f es nd n man t m t t ee si i n l s( ) ha b a sp T r e B ssel h co i si s o f g ti t This rouult ishows y haathhmatgcsarefertence s ooks.ecthum ewhicfunctnonsts fonea aseveof ord0.2 n < 0) are related to Bessel functions of positive order through er ( impulses that are located at the discrete frequencies ω = ±(ωc ± nωm ). The spectrum consists of an infinite numJ−r (x)s= ebann Jn (x)t are separated from the(1.51)er be n of id (−1)ds tha ca r r i . 4 freTuenterms Jnteg2thmuatiplesr on the fr6. reenicy oorthhempe1tlratm g atone, thmugThe q he cy by i (β )er at l ppea . i f the exp u ss on f8. t e sodc0. in c n be ω o . ht eq f uu n mod-als.tioeffiicients βhas just ra ine stanstrtengt h esceabhsothe epieak upsea. ePdotsiatiohe of u0a 2 on ndex t i t dete mcon the t ha t d of ri c e f th mp l h ss l ev of t n of c the esgelaflunThonsunctno= 0,n1,x) 3, 4calned5tare Bhown in ncitiure of2first kind of order n B si0.4 . cti e f for i n J ( 2, is , a l d he s essel fu F g on 1. 8. -s n. Theakinuntcteoins eare translatm ,ofathe fS (ωa giives avaaute rofati, e aorm off tJn (time- n Tse f g h i nv rse tabufored nd or ) g ven n l l e n n v t f bles o he x) ca be sfonaldthn tmiaaye yi2adhseoseaftiincsionstorendetrentfook=.0,1,hhp4,Beosedeflua ctinctsoof negfative m n gh . N c T , 5. o an ig un i a F gnr 1. e8:t Bes mle u cstirefe f or o e b hr t seac 2,3eair sf l t n fu on i ns at rem uy m l orderenny< 0)nawellrelietddatoermsoelthenfctrm s cospostitwhenrthe ithrerue hransform is qu ( c ±ω r i y a le t Be s f fu o ion2 of ωn ive o der nv o s g t 1.6 e 1 Exam appl.i2.d. Then ple - sinusoidally mo dulated signan l J−n (x) = (−1) Jn (x) Consider an angle-mo d∞ated signal of the form: ul 1 ∞ (1.51) j ω t the ex essio The terms(tJn (β ) that satppeacrcoisn2π2=t Acspr2π2t))n (fβ ) ctheωspe+t1nω)m tcan be tho52)ht s )= dω 0 Jn or os( c t c( rum ) (1. ug (S (= )e ) ωA n( 5 2πha−∞ etermine( the s+rein=−h of each of the im.p3 lses. Plots of the of as coefficients t t d t ngt ∞ u The carrier frequency for this signal is 20 Hz and the frequency of the mo dulating an angle-modulated signal of the form: s(t) = Ac cos(2π 20t + sin(2π 2t)) 36 C s sign . O MU C z O nSI NA e AND SY en MS ier frequency for thiHAPTER 1alCisM20NIHATIaN dGthLS frequSTEcy of the m Hz. The peak phase deviation associated with the signal (...
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