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ECE- 4603 http: //w w w . csc. gatech. edu/~copel and/4603 Pr of . John A . Copel and j ohn. copel and@ ece. gatech. edu 404 894- 5177 O f f i ce: GCA TT 579 em ai l or cal l M r s. KathyCheek, 4- 5696, f or

  1. ECE- 4603 http: //w w w . csc. gatech. edu/~copel and/4603 Pr of . John A . Copel and j ohn. copel and@ ece. gatech. edu 404 894- 5177 O f f i ce: GCA TT 579 em ai l or cal l M r s. KathyCheek, 4- 5696, f or of f i ce vi si t ti m e Suppl em ent to Chapter s 3 and 5 • A nal og to Di gi tal Conver si on • Bandw i dth ver sus Capaci ty • Nyqui st and Shannon equati ons. • Si gnal Degr adati on • Basebase and Br oadband Encodi ng Data & Com puter Com m . , p 95- 98, 148- 155 ECE4603 5a A nal og and Di gi tal Si gnal s A nal og Si gnal - val ue var i es conti nuousl y • Sound - ai r pr essur e w ave, can be conver ted to anal og vol tage or cur r ent w ave by m i cr ophone. • El ectr i cal (anal og) voi ce f r equency si gnal s - can be conver ted to sound by l oudspeaker . • Pi ctur e - l i ght (col or , br i ghtness) var i es conti nuousl y w i th posi ti on. Di gi tal Si gnal s - str i ngs of di scr ete val ues w hi ch can be r epr esented by bi nar y num ber s, str i ngs of one' s and zer os. • Ti m e- var yi ng anal og si gnal s ar e conver ted by aver agi ng the val ue over a ti m e i ncr em ent and assi gni ng a bi nar y val ue. • I m ages ar e di vi ded i nto sm al l ar eas (pi xel s), then col or and br i ghtness ar e aver aged over each pi xel and tr ansm i tted ar e stor ed i n di gi tal m em or y sequenti al l y. Conver si on of A nal og to Di gi tal Ti m e i ncr em ents, dt, m ust be sm al l enough to captur e hi ghest- f r equency com ponents of i nter est. The num ber of A m pl i tude I ncr em ents, n, m ust enough to gi ve an adequatel y- accur ate esti m ati on of the anal og si gnal . The bi t r ate i s n/dt (bi ts per second). Sam pl i ng ti m e = dt 7 = 0111 4 bi ts - > 16 l evel s 0 = 0000 m axi m um - 7 = 1111 bi nar y num ber s f or 0101 1101 1101 Bi t Str eam 0101 0101 1101 1101 0101 aver age val ue of = +5 = - 5 si gnal dur i ng dt i nter val s Reconstr ucti on Reconstr ucti on af ter l ow - pass f i l t er

  2. Di gi tal V oi ce • V oi ce i s r ecogni zabl e and i ntel l i gi bl e w hen f r equency r ange i s l i m i ted to 300 to 3400 Hz (Her tz = cycl es/second) and quanti zati on noi se < - 20 dB. • Tel ephone standar d i s to di gi ti ze 8000 ti m es per second (dt=125 m s) and to use 128 l evel s (8 bi ts i ncl udi ng si gn). • Thi s r esul ts i n a bi t r ate f or a voi ce channel of 64, 000 b/s. Di gi tal M usi c • M usi c r equi r es a f r equency r ange up to 18, 000 Hz and quanti zati on noi se < - 65 dB. • CD m usi c i s di gi ti zed 44, 100 ti m es per second (dt=23 µs) i nto 32, 000 l evel s (16 bi ts i ncl udi ng si gn). • Thi s r esul ts i n a bi t r ate f or a CD m usi c channel of 710, 000 b/s (ti m es 2 f or ster eo). A nal og and Di gi tal Si gnal s Di gi t al V oi ce 01100 A /D Channel Tel ephone Tr unk (Sound W aves) Bank 64 kb/s Di gi t al V oi ce 01100 I SDN 01100 I SDN Tr unk (Sound W aves) Tel ephone Sw i tch 64, 000 64 kb/s kb/s 01100 Anal og PC M odem Sw i tch RS- 232 28, 800 kb/s 0110010101100110 Channel Bandw i dth ver sus Capaci ty • Capaci ty = Rate i n bi ts/second (b/s) that bi ts can be tr ansm i tted. • Bandw i dth = Fr equency r ange (w i dth)of the channel (Her tz). • M axi m um Baud Rate (sym bol s/sec), B = 2 H • Noi se = Unpr edi ctabl e devi ati on of r ecei ved val ue due to al l causes (pr obabi l i ty bounded by acceptabl e er r or r ate). - Ther m al noi se, Cr osstal k, I m pul se, I nter m odul ati on, . . . • Nyqui st Theor em f or a noi sel ess channel : gi ven a bandw i dth H and a si gnal w i th L di f f er ent l evel s, the capaci ty C i s gi ven by: M axi m um Data Rate (bi ts/sec), C = 2 H l og 2 ( L ) • Shannon' s Theor em f or a noi sy channel w i th si gnal to noi se r ati o S/N i s gi ven by: C = H l og 2 ( 1+S/N )

  3. M axi m um Sym bol s ( Baud) per Second 1 1/R 0 1/2f Si nce Bandw i dth (H) = f m ax: Rm ax = 2 f m ax =2 H The m axi m um num ber of i ndependent ti m e i nter val s (sym bol s) i s equal to tw i ce the bandw i dth. Num ber of Bi ts per Sym bol 11 10 01 00 01 10 00 11 Tw o bi ts per sym bol r equi r es 4 l evel s. The num ber of bi ts per l evel , N bL , i s l og 2 (L). Level s Bi ts 2 1 4 2 8 3 16 4 32 5 64 6 1 0 0 0 1 0 1 1 01 1 0 1 0 01 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 1 Thi nk of a "Baud" as a "Bucket" that hol ds a cer tai n num ber of bi ts. The num ber of bi ts per second that pass a cer tai n poi nt (or ar r i ve at a node) = the num ber of Baud (Buckets) per second m ul ti pl i ed by the num ber of bi ts car r i ed by each Baud (i n each Bucket).

  4. Si m pl i f i ed Concept of Shannon' s Law The Capaci ty (m axi m um bi t r ate) i s equal to the m axi m um num ber of sym bol s per second (2 x Bandw i dth) m ul ti pl i ed by the num ber of bi ts per sym bol { l og2(L) }. - Nyqui st: C = 2 H l og2(L ) I ntui ti vel y, the m axi m um num ber of l evel s w i th an m axi m um si gnal vol tage V s i s appr oxi m atel y V s/V n, w her e V n i s the noi se vol tage (separ ati on vol tage betw een l evel s needed to r educe er r or s due to noi se to acceptabl e val ue). Cl aude Shannon (f ather of I nf or m ati on theor y) f ound a m or e exact val ue as a f uncti on of the r ati o of si gnal pow er S to noi se pow er N. Shannon: C <= 2H l og 2 ( (S+N)/ N) <= H l og 2 (S/N +1) to m atch Nyqui st: L <= (S/N +1) = (S+N )/ N L <= (si gnal + noi se vol tage)/(noi se vol tage) Pr obabi l i ty of r ecei ved l evel f or L=4 4 tr ansm i tted l evel s. V s=4V n V n Si gnal Degr adati on A l l r eal si gnal s ar e anal og by natur e. W hi l e the tr ansm i tter m ay send exact di scr ete l evel s i nto a physi cal tr ansm i ssi on l i ne, the r ecei ver sees a degr aded si gnal and m ust deci de w hi ch di scr ete l evel expected i s cl osest. 1 0 0. 2v 0. 0v A ttenuati on - l ost of str ength (am pl i tude) Bandw i dth cutof f - l ost of hi gh- f r equency com ponents. Data Tr ansm i ssi on Types A nal og Baseband A nal og Br oadband A M , FM , TV , Cel l ul ar (A M PS) • V oi ce Tel ephone • Di gi tal Br oadband Di gi tal Baseband Di r ect- TV (satel l i te) • I SDN V oi ce • • PCS, Di gi tal Cel l ul ar • Ether net Di gi tal CA TV • • PC Com m Por t 0 Fr equency 50 M Hz 1000 M Hz Baseband Br oadband

  5. Data Encodi ng Schem es Baseband - f r equency r ange i s f r om 0 Hz to f m ax (B = f m ax ) Br oadband - f r equency r ange i s f r om f m i n to f m ax (B = f m ax - f m i n ) W i th br oadband si gnal s, data i s m odul ated onto a car r i er w ave w hose f r equency i s at the center of the band. Com m on types of m odul ati on ar e: • A m pl i tude Shi f t Keyi ng (A SK) • Fr equency Shi f t Keyi ng (FSK) • Phase Shi f t Keyi ng (PSK) • Q uadr atur e Phase Shi f t Keyi ng (Q PSK) • Q uadr atur e A m pl i tude M odul ati on (Q A M ) W i th al l com m onl y- used Br oadband m odul ati on schem es: Bandw i dth (Hz) = Baud Rate (Baud/second) Br oadband M odul ati on Encodi ng A si ne w ave w i th ar bi tr ar y am pl i tude A and phase ø can be r epr esented by the am pl i tude of the i n- phase and quadr atur e com ponents, P & Q : V (t) = A si ne(w t+ø) = P si ne(w t) + Q si ne(w t+90) Q Q Q Q P P P P A SK Q PSK Q A M PSK 1 bi t 1 bi t 2 bi ts 4 bi ts Each state i s r epr esented by a dot i n the "constel l ati on" di agr am . Baseband Encodi ng Schem es Pr obl em s to over com e • Tr ansi ti ons needed to synchr oni ze r ecei ver bi t cl ock • DC r ef er ence l evel needs to be m ai ntai ned RZ - Retur n Good r ef . , doubl es to Zer o bandw i dth Tr ansi ti ons NRZ - Non not cer tai n RTZ Di f f er enti al : NRZ- I Pol ar i ty I nver ted i nsensi ti ve M an- Good ti m i ng, chester doubl es bandw i dth 0 0 1 1 0 1 Bi t str eam 30

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