Inboduction to Digital Communicahdns Why Digital Communicahans & + Prethy much most of the military ond Commeccial applicahans are going “DIGITAL. + Reasons: © The ease with which digital Signatc, Compared to analog signals, are regenerated. (see the Figure below.) LAAT | Bisa Senn oo = the shape of He original waveform (s affected by tum basic mechanisms: © the distorhag effect cue to the nonideal transfer funchtns of Hansmission Lines and Circuitt; © unwanted electrical noise or other interference further distorts tee pulse waveform. = Circuits that recover and regenerate tht original pulse at regular intewals along a -transmission sys are called repeaters® Digital circuits are less subject to disterhan ond intecferente than are analog Circuits, This is because binary digital circuits operate ch one af tur states, ov er OFE A disturbance must be la(ge enough fo Change the Circuit operahng point fom one state to another. This facilitates signal cegenerahtn and thus prevents noise and other disturbances from accumulahng ta transmission @ Analeg signals, on the otter hand, can take an icy of Shapes. With amalog Circuits, even a small Sisturban& can fender the reproduchdn of the wavefaum. @ Digital circuits ore moce eliable and can be prduted at Iswer Cost than analog Circuits ® Digital hardware lends inelf to much more flexble implementattn than analeg hardware , €-g-, micmproussort, digital Switching , and large-scale cntagrated CLST) Circuits © Mest ungortantly, different types sf cligital signale such as data, telegraph, telephone , dlevision Can be treated as identical signals cn transmission ond switching - obit @ In additdn, digital techniques allow ublizing Signal PRESSIng Hechniguo that pokect against interference and jamming Such as encryphtn ond Channel codingDisadvantages of Digital Transmission © Digital tansmissiBn typically requirer a greater System bandwidth as Compared to amaleg transmissidn. sr tromever, this con be Compensated for by adophag bondurdth eff cimt medulahtn schemes Gnere on this later) @ _ Digital detechon requires synchronizahon , whereas analog Signal: generally have no such cequiremant. ® Rongeaceful Degradation » @ Detinsive Comparators Blocle Diagram of atypical digital Comm. System + The folluong is a block diagram of o typical digtal Communicahdn System. ream : eww2A A digiveh communication supter (RCS) sends a waren from a Finite sex of gessihe wmreborns duning 9 Maite rateweh of Kime An Qnelig Communtation iaptem sends a mctonn af ~~ from on inkindre verity of careform chugs tai Pesvericdly, inhinte resolution Obyective ef DES Ts determine From a noise — pertureed siqash eich — wavekerm Ran Hae Rate sat ok trairhernns wed Seok Lag Bie ema renither Comoe so ve grduce a Bromsaitted wuieorn we, precision)+ Genes Comments en the block diagram the upper blecle (format thru multiple access) indicate the signal trnsfornahans from the source to He bransmithes the lewer blocks indicate the Signal trans formath@Bns from tha receiver to the Sink... They essentially reverse the Signal processing steps perfaimed by the upper blocs . - typically, ail The prowssing sleps shown usithin thea dashed Lines are refered to as O medemn Cshort for medulat/demedulator). In this case, the modem can be thought of ac the “brams” of the System. netle that chat Conshtuler a modem (s not a precise Contept - Some ab te blocks may or roy net be thee, depending on the applicahom. - the Tx BBX Con be thought of me the ‘muscles" of the system. - the TX usually Consists of 2 Frequency up-tonvertion Stage, a hygh-poser amplifies » and on antenna. Whireas the RX porhtn usually Consits of am antenna ; a low-noise amplifier , and a dawn— Converter stage+ Specific Comments on the block diagram - of all the Signal processing Steps, only formatting, modulahdn , and demodulahdn are essential for @ digital comm. system. The rest ore design optans for specific system needs. formatting : transforms te source tnfecmatan ‘mto digital gymbalk; it makes te unformahan Compatible csith the signal Processing vatthiin a digital Comm system. It usnally involves Sampling , guankahin , entediag , ete. = Medulatio: the proqss by Which He symbols ore Converted to waveforms that are Cempatible with the fransmission channel. - Source enteder: promssor which Converts the informahdn Ssurte , cohether amaleg or digital, to a representahin un digital farm as efficiently as possible, ce, minimizing the transmibteal redundancy (data Compression). - Encyphan: prevents unauthorized users fom understanding messages and from enjechng false messages into the system. - Choy der: digital processor which adds redundanty to the data to be transmitted , usually accordana ho Some mathematscal algorithm, with th goal ofprvidiag pokechdn against unavoidable , error—Cousing channel impairments Ceg-, noise, interference , fadiag , et.) - Multiplexing ond multiple access: procedures that Combine signals that. might have diffecent c/cs or might originake from different Soures So thay con share a porhdn of the Communicahin Vesey - Freguincy spreading: produces a signal that 1s less Volnurable 4o interference Choth natural and intenhdnal)) ond Can be used + enhane He privacy of the Communicators. = Synchnizahon: involves Carver Synch., Symbo} syoch. Cor ming recovery) » Frame Synch. , ete ~ & NOTE Hat the Signal procussing Steps Shawn ca tha block dicgvam represents a typical arrangement however, the blocks are sometimes Umplemented A adiffvent order, chpendiag on tht applicahinPerformante Criteria, Arateg: Fidelity i unporant Signal-fo-neise cahd Disterhan level Digital: — Pebabi of enoe (C bit/ symbol / Frame /tolocle error tate) Design Parameters — power = bandwidth - delay — Signal preassing / hardware Complexity Tools ~ Advoned Cmathimatcat) analy teal tech - Compater simulahdns jest beds - Advanced Circuit & device technology Coase, vist) with the advantement on technology » ee now pastibla to umplemant more Complex & sophisticated communitahon systems ko support new ServicesClass: Cahn of Signals © Deterministic and randem Signals - Delerminishe + exactly Known at any hme, 6g, HCH = tO tose = Random: « Some wn Cortasnity on its vob before if octurs , e.g-, XC) = mb) cont whee omct) is aspeech Signal. a4 described tn astatisthcaal sense tke to & VEL AED g pebabi @ Perddic and non-perisdic Signals ~ Peradic => xChtT) = x for Ft BT HO To is the pecdd Cone ful ycle) fo= Yr, fundamental frequency - — Nae penddic => ne value of Te that sabshes tho Condi hen =HeHSHe eit + penodtc non perdic @ Pnateg and Discrete Signals = Analog: XC) is“ Conkinusas for eh Hime | e4., speech _ Discrete: xc) or xCw) 18 defined only at Wseele Hmes , eg, a Sequena of numbers© Energy ond Power Sznals 20) ¢ _ instantanenas power * - pe) VE 2 COR wey FR & - if we let R=1 = normalized power wm pe = x5) where LHD. Can be valtoge or Current average Power We Poy = em { xo dt Ta Ath if the signal is peritdic, the average Power Can be Calculated over ane peridd Tw = fy - 1 ff alee dt Paty, te perdd ef the signal. where Te is of power over bine _ eneegy is We € =e Xap at Boe 2 Ye - ents? over aw Es &T te if C = % if o< RS =» xc) is10 KG) = A CosCemht) , ect dos ynat 2 is xCH energy or poser Aes Since XC) is pevddic with perad T= Ye we xen ( xt de We ~ wo = + g PP cos ax fat) dt “he Me Lf CAE v Be cos canted) dt " -t%, We Ae} ne j tos Uae de yp Ae 2T “Me Th Seren Pas cintegemted even one inkerval —> =o -flE-Cw)I - Ae oe Sine oc Ry <= OKC IS aw power Signal a « xe & 2 mer = JAS troy ee en 2 a b ee fxm = fred . LL gy Ok Em ae energy Signal tae oe Leer 2 bnEx 3 KG) = utp xt) = uO) ' > | » > o, teo Ws he e = ba f Red Line f ater - Tee oy Tose Wa e be &l = Ln % Tae 8 To o We Be bm bk fxtemae 2 Din be Dy ron Ty, T0 se othe Unit Shp te a power Signal. a Aluttre -uceo] xr Bed a) = e Aaleet? es Fxteae A 2 lit .. 2 ( Atde * Autrey = A . wel x 2 arte = Energy Signal Genera Rove: - perddic signals are power signals ~ determinate 6 nonpenddic =p energy Sigaals = fandom Signals are usually piwer signalsThe Unit Umpulse funchdn Cor Dirac delta fanchon $cH) = Vey usefid tn Communicahon theory - Tt ts an infinitely lage amplihade pulse , with 2e@ pulse width ond unity wesght - Pepeches sf sce): tig Orta et © Sse de “Ue We -7 ar aren 2! @ swp-0, t#o a SH) 2% , rm sa @ §[ KwHSle-coydt = xed ‘ Ly thie is called sifting or Samphng propery Asle-te) 1 SpecteaL Densrry Distributdn of Signal energy or power om the Frequenty dernain. ~ Energy Spectral Density CESO) Signal power per unit bandwidth C T/He) = fen af “ew Signal Energy E = J apd ~*Br Key XCF) [xceni® is the enecgy Spectral density, WCF) => © = fret df ~ For real-valued Synals, XCF). is even => YF) = | xUp)' is alse even > €22 Jucpap 3 — Power Spechal Density Signel power per ani bandwidth (v/ He) For penddic signals , Te “ Roe (tarde 2 Zo Veni® Te a % where Te is the petidd and Ca are te @mplx Fourves secies Coefficaats defined as = jem ht xe) = 2 Gre » Ae he We -jexnfet 3 Gat fane dt “WePSD fer perddic Synas is defined as « GC) = 2. IG S Chen fe =~ Sema - f x lent SCF-nfa) af a oe «© \ 2 lea J Sefenfe) dF Ze = F jou RR =» The average power “ Re = (6,0 oF Se xeey 2 A Cos 2x fe je ae but use = Exe = fo 5 Sethe | exhe Jes = Re Be LA a MD = XCF) 2 FTL pen} ASCEf) + A SCF ef) St = We Ae XO Me G20, 20,22, 48, OE = GCP 2 (A sce rh) + (A) 5CF- fe)2 a, = J GCap a0 . fF AE seen) ap + f Ab Slee te uf “ a Az 2 AR +. z z ary 7 UTOCORRELATION Provides a measure of how a signal matches adelayed versian of itself. Energy Signals Creal- valued) e,cx = Smxcerde — ~wc tS “= R.Ce) ts not a funchan of hme. Th is ony a funchan of the Knie difference t => Prpertes of Rr) for real-valued energy signals @ Symmetry — &e-w) = RCO * ® Signal enesy - E= Roo) = { xcyde a @® max. @ origin - ReCe) < Rx Co) @ sD i FT of Ree) aco Eb, Uce ace = J Ree LitePower Signals We Rele) = bm Lf xcrgcerer de — werden eT) if xc is Qecddie, with perdd T, Te Re = tf xeer aces de We => properties of RCo) for real-valued penddic signals: © symmetry a Rec) = Re led ® RKRelt) SF RCo} er @ Rl a> ote) poses spectral damsity Ty cPs0) D be Mo- + § xtoae “Te EX Find RCT) and PSD for Kid = A Cos(2mht) Sr KE) 1s peddle % Ree) = a fneacersae % Wye pe f At Cos @xhi)- Cos@x Actst)) dé we ™ 9? 2 AY VS csaxhrdt at J ystunhe re) de tan are Sy We Pt cosampe ot | ate “hyeGCF) = ETL Roy + FF ACh) 4 AE ScFeRD = fy = Sacmap 2 ay Note For non-penddic power signals - no fourier series representaten ne Fourier Wansdevm representehan se Te gek around Huo, defie a Sp an the Limit ey generahng oa truncated version of the Signal Such Heat the energy ts finite end has a FT. ) ) TWh see Y, Mee) = ye = ° eau. XPD = FTF mews = PSD! Gece = ee L | CH? Teo % Sagoncersyae Ve Also, Rele) Stem RICE), cohane ReCa) #