アナログ変調の品質評価 - ist.aichi-pu.ac.jp

1 (shot noise) Si( )=qI0 I0: Sv( )=2kTR (| |<<2 kT/h) 100MH n(t)=nc(t)cos ct-ns(t)sin ctnc(t) ns(t) cos ct n(t) cos ct=1/2 nc(t)+1/2[nc(t) cos2 ct -ns(t)sin2 ct][n(t) cos ct]LP= 1/2 nc(t) LPLow Pass nc(t) nc(t) Snc( ),n(t) Sn( ) [n(t) cos ct]LP= 1/2 nc(t)[n(t)(ej ct+e-j ct)/2]LP= 1/2 nc(t)[n(t)(ej ct+e-j ct)]LP= nc(t)Snc( )= [n(t)(ej ct+e-j ct)]LP = [Sn( - c)+ Sn( + c)]LP ns(t) Sns( )Sns( )= [Sn( - c)+ Sn( + c)]LPnc2(t) = ns2(t) n2(t) = ns2(t) + nc2(t) n2(t) =ns2(t) =nc2(t) AM SN SN Signal to Noise ratio ( c ) SN DSB-SC SN SN Suppressed Carrier Double Side Band maAs1(t)cos( ct+ c)

2 C 0 si(t)= f(t) cos ct Si={f(t) cos ct}2=1/2 f(t)2 si(t)cos ct= f(t) cos2 ct=1/2 f(t)+1/2 f(t)cos2 ct s0(t)=1/2 f(t) S0=1/4 f(t)2 =1/2Si ni(t)= nc(t)cos ct-ns(t)sin ctNi=[1/2 nc(t)2 + 1/2 ns(t)2] =n2i(t) no(t) [ni(t)cos ct]Lp no(t)=1/2 nc(t)No=1/4 n2c(t) =1/4 n2i(t) =1/4Ni SN SN So/No= 1/2Si /{1/4 Ni}=2 Si/Ni SSB-SCSuppreesedCarierSigleSide Band SN si(t),Si, so(t), So, ni(t), Ni, no(t), No si(t)=f(t)cos ct f (t)sin ctf (t) f(t) Si=1/2f2(t) + 1/2{f (t)}2 f (t) f(t) |F( )|2=|F^( )|2 f2(t) ={f (t)}2 Si=f2(t) SSB 190 90 2 2+ 1(t)= (Ama/2)cos{( m+ c)t+ c}+(Ama/2)cos{( m- c)t+ c} 2(t)= (Ama/2)cos{( m+ c)t- + c} +(Ama/2)cos{( m- c)t+ c} 1(t)+ 2(t)= Amacos{( m- c)t+ c} 1(t)- 2(t)= Amacos{( m+ c)t+ c} :f(t)/2So=1/4 f2(t) =1/4Si DSB-SC.

3 No=1/4 n2c(t) =1/4Ni SN So/No=Si/Ni SSB-SC DSB-SC Sso, Ssi, Nso, NsiSdo, Sdi, Ndo, Ndi Ssi=SdiSSB-SC Nsi=Ndi/2 SSB-SC SN Sso/Nso=Ssi/Nsi= Sdi/(Ndi/2)= 2 Sdi/Ndi= Sdo/NdoSSB SDB AM si(t) {A+f(t)}cos ct si(t)+ni(t)={A+f(t)+nc(t)}cos ct-ns(t)sin ct=Re{R(t)ej( ct+ (t) }=R(t)cos( ct+ (t))R(t) (t) A+f(t)R(t)nc(t)ns(t)-ns(t)sin ct=ns(t)cos( ct+ /2)n(t) (t) R(t) (t)R(t)= {A+f(t)+nc(t)}2+ns2(t) (t)=tan-1[ns(t)/{A+f(t)+nc(t)}] SN A+f(t)>>nc(t), ns(t)R(t)=A+f(t)+nc(t) (t)=ns(t)/{A+f(t)+nc(t)} A+f(t)R(t)nc(t)ns(t)-ns(t)sin ct=ns(t)cos( ct+ /2)n(t) (t) SN A+f(t)<<nc(t), ns(t)rn(t)= nc2(t) ns2(t) (t)=tan-1[ns(t)/nc(t)]R(t)=rn(t)+{A+f(t)}cos (t) cos (t) A+f(t)R(t)nc(t)ns(t)rn(t) (t) FM SN FM si(t)=Acos{ ct+kf tf( )d } Si=1/2 A2 si(t) so(t)= d { ct+kf tf( )d }/dt- c=kff(t) So=k2ff2(t) FM 2 Rxx(0)=1/2 xx( )d pp32 xx( ) N/2 Ni=N / No f(t)=0 {A+nc(t)}cos ct-ns(t)sin ct=Re{R(t)ej( ct+ (t) }=R(t)cos( ct+ (t))R(t)= {A+nc(t)}2+ns2(t) (t)=tan-1[ns(t)/{A+nc(t)}] No R(t)= {A+nc(t)}2+ns2(t) (t)=tan-1[ns(t)/{A+nc(t)}] A>> nc(t),ns(t) (t)= ns(t)/A no(t)=d (t)/dt=1/A dns(t)/dt H( )=j Sno( ) Sns( ) Sno( )=1/A2 Sns( )|H( )|2= 2/A2 Sns( ) No Sno( )= 2/A2 Sns( )= 2/A2 [Sni( - c)+ Sni( + c)] f(t) | | m Sno( )= 2/A2 [Sni( - c)+ Sni( + c)]| |> m Sno( )=0 Sni( - c)=Sni( + c)=N/2 Sno( )=N 2/A2 (| | m) No=1/2 - m mN 2/A2d =N m3/(3pA2) SN Si=A2/2, Ni=N / Si/Ni= A2/(2N ) So=k2ff2(t) ,No=N m3/(3pA2)So/No=[3pA2k2ff2(t) ]/(N m3)))

4 SN So/No=[6k2f f2(t) ]/( m3) Si/Ni FM AM SN f2 (t) Sni=N/2AM 2 mNi=N m/ AM SN (So/No)AM= f2 (t) /(N m)FM So/No (So/No)FM=3(Akf/ m)2 (So/No)AMf(t)=acos m akf/ m= / m=mf(So/No)FM=3mf2 (So/No)AMFM AM SN 3mf2 FM W=2( + m)= 2 m ( / m+1)= 2 m (mf+1)AM (mf+1) mf=5 (mf+1)=6 SN 3mf2 =75 FM A>>nc(t), ns(t) CN Carrier to Noise ratio FM si(t)+ni(t)=Acos{ ct+ (t)}+rn(t)cos{ ct+ (t)} si(t)+ni(t)=Acos{ ct+ (t)}+rn(t)cos{ ct+ (t)} si(t)+ni(t)=R(t)cos{ ct+ (t)+ (t)} (t)=tan-1[Asin{ (t)- (t)}/{rn(t)+Acos( (t)- (t))}]CN A<<rn(t) (t)= A/ rn(t) sin{ (t)- (t)} d (t)/dt+d (t)/dt d (t)/dt (t) rn(t) (t) (t) R(t)rn(t) (t) (t)- (t) (t) (t)Ans(t)nc(t) SN preemphasis deemphasis preemphasis deemphasis deemphasis Deemphasis (vo/vi)Hd( )=1/(1+j / 1) 1=1/RC SN Sno ( )= N 2/A2 |H( )|2| | mNo =1/2 - m mSno ( )d = N/A2 0 m 2/{1+( / 1)2}d 1|H( )|vivo So So SN = (So /No )/ (So/No)= (No/No )=1/3 {( m/ 1)3/[( m/ 1)-tan-1( m/ 1)]}SN m/ 1 SN PAMPAM LPF so2(t) =k12 si2(t) no2(t) =k12 ni2(t) So/No=Si/Ni PTM (t)/tr=ni(t)/A (t) PPM No= 2(t) = (tr/A)2Ni f(t) S0=k22f2(t) k2 Si=( /Ts)A2t (t)trA + ni SN So/No=Tsk22f2(t) /( tr2) Si/Nitr tr ( ) tr SN