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1 Lct # Pl s. Li bdsid s with ifm mplitd distibtis. Gl Csidtis Uifm Bimil Optimm (Dlph-Tchbshff) Cicl s. Pl s ssmig ifm mplitd citti m F m d cs z F d d M COMM Lct #
2 Pl s ssmig ifm mplitd citti F m m m T vid gtig lbs th spcig shld b lss th hlf wvlgth i bth pls. Mimm d cs M d M Th phss idpdt f ch th th c b dstd t hv th lcti f th mimm t th sm gl. I mst pcticl pplictis it is qid tht th mi bms f bth fcts itsct d thi mim b dictd twd sm dicti. Pl s F mimm t spcific gl d cs & d d t d d d COMM Lct #
3 COMM Lct # Pl s: Dictivit m m m F * * d d F F F F D D D D cs Wh D d D th dictivitis f bdsid li s ch spctivl f lgth d mb f lmts L M d L. Th c fct ccts f th dcs f th dictivit bcs th dcs f th pctd f th. Uifm Sm mplitd d phs. Uifm distibti ilds th mimm dictivit gi. Fist sid-lb lvl is % f th mi lb mimm. ) ( F =
4 Uifm ts f ll pplictis Jh D. Ks & ld J. Mhf Bimil mplitds pptil t th cfficits f bimil sis b =mb f scs. b b! mi lps. Icsd Bmwidth. Lg ti f ct tis ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct #
5 Bimil Pscl Tigl = = = = = = 6 = = 8 = 9 = = = = = w w 6 w w 8 w 9 w w w w dg d Mi lps Sm s M Lp. Smll Bmwidth ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct #
6 Optimm (Dlph-Tchbshff) If th sid-lb lvl is spcifid th bmwidth btw fist lls is miimizd If th bmwidth btw fist lls is spcifid th sid lb lvl is miimizd ts f ll pplictis Jh D. Ks & ld J. Mhf Li bdsid s with ifm mplitd distibtis. Gl Csidtis ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct # 6
7 Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti v mb f scs cs cs d cs d cs cs wh s tht cs ts f ll pplictis Jh D. Ks & ld J. Mhf Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti Odd mb f scs cs cs wh cs cs / ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct #
8 mpl i Istpic Scs Hc Odd scs d Sm mplitd d Phs cs cs cs cs cs cs cs cs Scs Spcig Fi tm Ptt Cstt Cicl Fdmtl lbs Scd Hmic 8 lbs Thid Hmic lbs Fth Hmic 6 lbs ts f ll pplictis Jh D. Ks & ld J. Mhf mpl ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct # 8
9 m T m Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti Tchbschff Plmils ( ) cs m cs cs cs cs cs cs cs 8cs 8cs cs 6cs cs cs m cs 6 cs6 cs 8cs 8cs cs 6cs cs 6cs cs 8 6 cs8 8cs 6cs 6cs cs cs9 6cs 9 6cs cs cs 9cs cs 8 T m () cs Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti T m T m ( ) cs ( ) csh m csm cs ( ) m cshm csh ( ) Tm ( ) Tm ( ) Tm ( ) t: csh ( ) l / ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct # 9
10 Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti Th pptis: ll plmils f d pss thgh th pit (). F vls f i th g - + th plmils ll li btw dit vl f + d -. ll ts cc btw - + d ll mimm vls i this g. Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti Dsig bdsid Dlph-Tschbschff f M M+ lmts with spcig d btw th lmts. Th sid lbs db blw th mimm f th m lb. Fid th citti cfficits d fm th fct. Pcd: () Slct th pppit fct (dd v). cs / Is plmil f dg + cs / Is plmil f dg COMM Lct #
11 Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti Pcd: (ct.) () pd th fct. plc ch cs(m/) fcti (m= ) b its pppit sis p. () Dtmi th pit = sch tht T m ( )=. Th dsig pcd qis tht th Tschbshff plmil i th - wh is th ll st t =+ b sd t pst th mi lbs f th. Th m lb f th ptt is fmd fm th miig pt f th plmil p t th pit ( < ). mpl mi lb mimm sid lb lvl T ( ) m ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct #
12 COMM Lct # Li s with ifm mplitd distibtis. Th Dlph-Tchbschff Optimm Distibti Pcd: (ct.) () Sbstitt i th fct f stp s t = it ttis its mimm vl f it. () qt th fct fm stp ft th sbstitti f stp t T m () this will llw th dtmiti f th citti cfficits f th. (6) Wit th fct i () g th cfficits fd i stp. cs mpl if =8 i phs istpic scs spcd / pt d t hv sid-lb lvl 6 db blw th mi-lb mimm. Fid: () Th mplitd distibti flfillig this qimt tht pdcs th miimm bmwidth btw fist lls (b) th HPBW d (c) th gi. sw: cs cs cs cs cs cs / cs 6 cs 6 6 cs cs 6 6 6
13 mpl W qt t th plmils T 6 6 Fid th vl f sid lb lvl ( db) lg 6 ( ) T ( ) csh csh csh csh (). 8 T Th ltiv mplitds f th ight scs giv b mpl.6cs.cs cs.cs cs cs ts f ll pplictis Jh D. Ks & ld J. Mhf COMM Lct #
14 COMM Lct # Cicl z z ) ( z z ˆ ) ( ) ˆ ( ) ˆ ( ) ( ) ( ) ( z z z cs cs Cicl cs cs cs cs cs cs cs cs cs ) ( I citti cfficits (mplitd d phs) f th lmt lmt f ttl lmts fct
15 Cicl F I cs T dict th mi bm t ( ) F cs I F cs cs I cs t cs cs cs cs / COMM Lct #
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