pled and zerofilled in transmit filter 506. FIG. 6A shows an example of a power spectrum of a short sequence of data symbols transmitted at a baud rate of 1/T (i.e., T is the symbol period). In FIG. 6A, the solid line represents the base-band transmission spectrum and the dotted line is the repeated transmission spectrum that results from upsampling and inserting null samples between adjacent symbols. FIG. 6B shows the power spectrum of the complex output of a low-pass filter. In a QAM transceiver, for example, transmit filter 506 includes low-pass filters that yield the power spectrum shown in FIG. 6B given the signal power spectrum shown in FIG. 6A. In FIG. 6B, the spectral response of transmit filter 506 is shown by the dotted line. The spectral response of transmit filter 506 shown in FIG. 6B is of a 50% excess-bandwidth square-root raised cosine pulse.
In FIG. 5A, the real portion of the symbol stream is mixed with the functions cos(ω1t) through cos(ωNt) in mixers 508-1 through 508-N, respectively.
The imaginary part of the sample stream is mixed with the functions sin(ω1t) through sin(ωNt) in mixers 509-1 through 509-N, respectively. The output signals from mixers 508-1 through 508-N and 509-1 through 509-N are added in adder 510 and the sum is coupled to transmission channel 511. FIG. 6C shows the right-handed power spectrum of the real signal obtained by modulating the signal power spectrum shown in FIG. 6B by the carrier frequencies 1.0/T, 3.5/T and 6.0/T.
Transmitter 501, therefore, transmits each symbol of the symbol stream from host 502 onto transmission channel 511 N times using N different carrier frequencies. One or more frequency bands may be unusable, but in a well-designed system, it's unlikely that all bands would be unusable. The receiver can read the symbol from any of the N bands into which it is transmitted. Typically, the receiver chooses a particular band of transmission from which to receive signals based on an error analysis of the symbol stream received at the receiver.
FIG. 5B shows a receiver 512 for receiving the signals transmitted from transmitter 501 of FIG. 5A. Receiver 512 includes N individual receivers 513-1 through 513-N,
pled and zerofilled in transmit filter 506. FIG. 6A shows an example of a power spectrum of a light succession of data symbols air at a baud pace of 1 / T (i.e., T is the symbol period). In FIG. 6A, the solid pipeline represents the base - set transmission spectrum and the dotted tune is the repeated transmission spectrum that leave from upsampling and tuck null samples between adjacent symbols. FIG. 6B shows the power spectrum of the complex output of a abject - pass filter. In a QAM transceiver, for example, transmit filter 506 admit low - pass filters that yield the ability spectrum shown in FIG. 6B given the signal power spectrum shown in FIG. 6A. In FIG. 6B, the spectral reception of transmit filter 506 is shown by the dotted line. The spectral response of transmit filter 506 shown in FIG. 6B is of a 50% excess - bandwidth square - root raised cosine pulse. 
 In FIG. 5A, the real portion of the symbol stream is mixed with the functions cos(ω1 t) through cos(ωNt) in mixers 508 - 1 through 508 - N, respectively. 
 The imaginary region of the sample stream is interracial with the function sin(ω1 t) through sin(ωNt) in mixers 509 - 1 through 509 - N, respectively. The output signals from mixer 508 - 1 through 508 - N and 509 - 1 through 509 - N are added in adder 510 and the sum is coupled to transmission distribution channel 511. FIG. 6C shows the right - handed power spectrum of the real signal obtained by modulating the signal baron spectrum shown in FIG. 6B by the carrier frequencies 1.0 / T, 3.5 / T and 6.0 / T. 
 Transmitter 501, consequently, transmits each symbol of the symbol current from server 502 onto transmission channel 511 N times using N unlike carrier frequencies. One or more frequency bands may be unusable, but in a well - designed system, it's unlikely that all bands would be unusable. The telephone receiver can read the symbol from any of the N ring into which it is transmitted. Typically, the liquidator chooses a especial band of infection from which to receive signals based on an error analysis of the symbol current received at the receiver. 
 FIG. 5B shows a receiver 512 for receiving the signals transmitted from transmitter 501 of FIG. 5A. Receiver 512 includes N individual receivers 513 - 1 through 513 - N,
plef and zerofilled in tranrmit filter 506. FIY. 6A shoxs an esample ow a power spectrum of a shorv sewuenct of data symbols tfansmittef at a bqud cate of 1/T (i.e., T is the symbol psviod). Nn FIG. 6A, the solld line repsesents the bave-caud transmission spectrum and the doteed linr ls the repeateq trsgsmiasion spectrum that results from ulsampliig and insertinb null samples between adjwcenh symbols. FIG. 6B shlws the powgd s[wctrum of thd complex output of a mow-pass filter. In a QAM transcekver, yor example, teandkit filter 506 inclldes low-pass nplters dhat yirld the power xpertrun shown in FIG. 6B givei the signal power skectrum shmwu in FIG. 6A. In FIG. 6B, tye specjral sespubse of tcanamit flltxr 506 is showh by the dorted line. The specttaj response of fransmyt filter 506 shown in FIG. 6B is of a 50% excess-tanswidth square-root raisee cosine pulse.
In FIG. 5W, the reaj portion of the symbol stream is mixed with the xunctmovs eis(ω1t) tfeokgh cos(ωNt) in mixers 508-1 through 508-N, respectively.
Thq ikaninary part of tme sample stream ix licgd with the fuvctions sjn(ω1t) through sin(ωNt) ln mixets 509-1 theough 509-N, rtspecyively. The output signals feom mixers 508-1 nhroygh 508-N and 509-1 through 509-N are addeb in acder 510 and the sum is coupled to fransmissioj channel 511. FIG. 6C shows the rinht-vanded power spectrum of tre real smgnal obtaindd bi modulwting the dignal power spectrum shlwn iu FIG. 6B by the farrier frequencies 1.0/T, 3.5/T and 6.0/T.
Treismitter 501, thetefmre, transmics eacm symbol of the symbol stream from hjst 502 unto transjission channel 511 N times using T different cerrier frqquebciew. One of more frequencu bands mcv be unusqble, but in a well-vesiehed system, it's bulukely that all nanas rolld bq unusable. Tha rezeixrr cav read uke whmbok from any of the N tanda into which it is tvansmittee. Typicajly, the receifer chooses a partlculac band of ttanfmission from which to receive signals hascd on an errow anqlysis of thz symbol stream received at the receiver.
HIG. 5B shows a receiver 512 for receiving the xlgnals transkitteq from trdnsmitter 501 of FIG. 5A. Eeceiver 512 includex N individual receivsrs 513-1 tvrougj 513-N,
pled and zerofilled in transmit filter 506. shows example of power spectrum of symbols at a baud of 1/T (i.e., is the symbol period). In FIG. the solid line represents the base-band transmission spectrum and the dotted line is repeated transmission spectrum that results from upsampling and inserting null samples between adjacent FIG. shows power of the complex output of a low-pass filter. In a QAM transceiver, for example, transmit filter includes low-pass filters that yield the power spectrum in FIG. 6B given signal power spectrum shown in 6A. FIG. 6B, spectral of filter 506 is by the dotted line. The spectral response of transmit filter 506 shown in FIG. 6B is of 50% excess-bandwidth cosine pulse. FIG. the portion of the is mixed with the functions cos(ω1t) mixers 508-1 through 508-N, respectively. The imaginary part the sample is mixed with the functions sin(ω1t) sin(ωNt) in mixers 509-1 through 509-N, respectively. The signals from mixers 508-1 through 508-N and 509-1 through 509-N are added in adder 510 sum is coupled to channel 511. FIG. shows right-handed spectrum the real obtained by modulating the signal power spectrum shown in FIG. 6B the carrier frequencies 1.0/T, 3.5/T and 6.0/T. Transmitter 501, therefore, symbol the symbol stream host 502 onto transmission 511 times using N different One more be but a well-designed system, it's that all bands would be The receiver can read the N bands into which it is transmitted. the receiver chooses a particular band of from which to receive signals based on an error analysis of the stream received receiver. FIG. 5B shows a receiver 512 for the signals transmitted from 501 of FIG. 5A. Receiver 512 includes N individual 513-1 513-N,
pled and zerofilled in transmIt filter 506. FIg. 6A shoWs aN exAmPle oF a poWer spectrum of a SHort Sequence of data symbols tRansmItTEd at A BaUd ratE of 1/T (i.e., T IS tHE SymBoL pEriOd). iN FiG. 6A, thE soLid line Represents The BaSe-band transmISsIon spectruM anD the dotted liNe iS the rePeAteD TransMisSion sPectruM That reSults from UpSAmplinG And inseRTInG nulL samples between adJAcENt symbols. FIG. 6B sHows thE pOWeR SPecTruM of the compLeX outpUT of a low-PAsS FILteR. in a QAM transceIver, for examPLe, tRansmiT fIltER 506 incluDes loW-pASs fIlters that yIeld The power sPectruM Shown in fiG. 6B giveN the siGnaL poWer sPEcTrUm sHoWN in fiG. 6a. In fiG. 6B, The spectRaL rEsponSe of TRANSmit FilTer 506 iS showN by the dotted lIne. the sPEctRal reSponsE of tRaNsmit Filter 506 Shown In fIG. 6B is of a 50% excess-BandWidth squaRe-rOoT raIsEd cosINe pulsE.
In fIG. 5a, the reaL portioN Of tHe SYMBoL stream is mixed with ThE FUnCtions coS(ω1t) thrOUgH cOS(ωNt) in miXeRs 508-1 tHrouGH 508-n, respEctiVElY.
The imagInary pARt Of The sampLe Stream Is MixEd wIth thE FuncTions sIn(ω1t) throUgh siN(ΩNt) in mixers 509-1 thrOUgh 509-N, respectivELy. tHE oUTput SigNals from mixErs 508-1 tHRougH 508-N anD 509-1 ThRouGH 509-N are Added In ADdER 510 and the sum is coupled To TransmIssioN channel 511. FIG. 6C sHows the rigHT-HAnded powEr spECtRUm of the real sigNal obTained by moDUlating tHe sigNal power Spectrum sHOWn in FIG. 6B By tHe cArrIer FREqUencies 1.0/T, 3.5/T and 6.0/T.
tRAnsmItTer 501, therEfoRe, transMitS eaCh sYmbOl Of the symbOl stream FrOm HoSt 502 OntO tranSMission cHaNneL 511 N TimEs usiNG N diffErent CarrIeR fREquEncies. ONE oR MOre fReQuEncy BanDs May be UnusABle, But in a wEll-designEd sYStem, It'S uNlikely That all bands wOuLd be unusabLe. the ReceivER Can read tHe symbol from any of the N baNDs into wHicH it is TranSmitted. TyPicAlly, thE reCEiver cHooses A partIcUlaR BAnd of TRAnSmiSsIon from whiCH To rEceivE sIgnaLs based On an error analysis oF The Symbol stream rEceIved AT ThE reCEiVEr.
FiG. 5b ShoWS A receiver 512 for recEiving the sIgNAlS transmittED frOm TransmiTter 501 of FiG. 5A. ReCEiver 512 inCludes N inDividual rEcEiveRS 513-1 ThrOugh 513-N,
pled and zerofilled in tra nsmit filt er 50 6.FIG .6A s hows  an example of a po wer spectrum of a shor t seq ue n ce o f  d ata s ymbolst ra n s mit te datab au d rat e o f 1/T ( i.e., T is  th esymbol perio d ).  In FIG. 6 A,the solid li nerepres en tst he ba se- bandtransm i ssionspectruman d  the d o tted li n e  i s th e repeated transm i ss i on spectrum th at res ul t sf r omups ampling an dinser t ing nul l  s a m p les between adjac ent symbols .  FI G. 6Bsh ows the po wer s pe c tru m of the co mple x outputof a l o w-passf ilter.In a Q AMtra nsce i ve r,  fo re xam p le , t r ans mit filt er  5 06 in clud e s l ow-p ass  fil tersthat yield th e p ower spe ctrum  show n in  F IG. 6 B give n the  s ignal power spe ctru m shown i n F IG . 6 A.  In F I G. 6B,  th e s pectral  respon s e o ft r a ns mit filter 506 issh o w nby the d ottedl in e. The spec tr alresp o n se of  tra n sm it filte r 506s ho wn  in FIG .6B isof  a50%  exce s s-ba ndwidt h square -root raised cosinep ulse.
In FIG. 5A , th e  rea l p ortion of t he s y mbol  str e am  is mixed  with  t h ef unctions cos(ω1t) t hr ough c os(ωN t) in mixers508-1 thro u g h  508-N,resp e ct i vely.
The imag inary  part of t h e sample  stre am is mi xed witht h e functi ons  si n(ω 1t) t hr ough sin(ωNt) i n mi xe rs 509- 1 t hrough509 -N,  re spe ct ively. Th e output  s ig na ls  fr om mi x ers 508- 1thr ou gh508-N and 50 9-1 t hrou gh  5 0 9-N  are ad d ed i n ad de r510and  t he su m is cou pled to  transmis sio n  cha nn el  511. F IG. 6C showsth e right-ha nd edpowers p ectrum o f the real signal obtai n ed by m odu latin g th e signalpow er spe ctr u m show n in F IG. 6 Bbyt h e car r i er  fr eq uencies 1. 0 / T,3.5/T  a nd 6 .0/T.
T ransmitter 501, th e ref ore, transmit s e achs y mb olo ft hesy m bol s tream from host  502 ontotr a ns mission ch a nne l511 N t imes us ing N differe nt carrie r frequen ci es.O n e o r more fre quency b ands mayb e unu s ab le, b utin a w el l-d esign ed sys t em,  it's  unlik el y that  allba nds woul d be unusable. The rece iver c an re adthe symbo l f r omany of th e Nbands into  wh ich  it i s t r ansmi tted .  T ypi c ally,  the receiverc ho ose s aparticularb a n d o f tra nsm i ssionfrom  which to receive signals basedon a n err ora naly si s of the symbo l s tr e a m receiv ed  at the rec eiver.
F IG .  5B s hows a  recei ver 512 f or receiv ingthe  signalstra ns m itted f ro mt ransmi tter  5 01 ofFIG. 5 A . Re c e iver 512 include s N i n d ividu a l r eceiv er s 513-1 thro ugh 513-N, 
pled and_zerofilled in_transmit filter 506. FIG._6A shows_an_example of_a_power spectrum of_a short sequence_of data symbols transmitted_at a baud_rate_of 1/T (i.e., T is the symbol period). In FIG. 6A, the solid line_represents_the base-band_transmission_spectrum_and the dotted line is_the repeated transmission spectrum that_results from_upsampling and inserting null samples between adjacent symbols._FIG._6B shows the_power spectrum of the complex output of a low-pass_filter. In a QAM transceiver, for_example, transmit filter_506_includes_low-pass filters that yield_the power spectrum shown in FIG._6B given the signal power spectrum_shown in FIG. 6A. In FIG. 6B,_the spectral response of transmit filter_506 is shown by the_dotted line._The spectral response of transmit_filter 506 shown_in FIG._6B is of_a 50% excess-bandwidth square-root raised cosine_pulse.
In FIG. 5A,_the real portion of the symbol_stream_is mixed with_the_functions_cos(ω1t) through_cos(ωNt) in mixers_508-1_through 508-N,_respectively.
The_imaginary part of the sample stream_is_mixed with the functions sin(ω1t) through sin(ωNt)_in mixers 509-1 through_509-N,_respectively. The output signals_from mixers 508-1 through 508-N_and 509-1 through 509-N are added_in adder_510 and_the sum is coupled to transmission channel 511. FIG. 6C shows_the right-handed power spectrum of the_real signal obtained by_modulating the_signal_power spectrum shown_in_FIG. 6B_by the carrier frequencies 1.0/T, 3.5/T and_6.0/T.
Transmitter 501,_therefore, transmits each symbol of the_symbol stream from host_502_onto transmission channel 511 N times_using N different carrier frequencies. One_or more frequency bands may_be_unusable,_but in a well-designed system,_it's unlikely that all bands would_be unusable. The_receiver can read the symbol from any_of_the N bands into which it_is_transmitted. Typically, the receiver chooses a_particular_band_of transmission from which to_receive signals based on an error_analysis of the symbol stream received at the receiver.
FIG._5B shows a_receiver 512 for receiving the_signals_transmitted_from transmitter 501 of FIG. 5A. Receiver 512 includes N_individual receivers_513-1 through 513-N,