Jos_von_Asmuth_Thesis.pdf - repository

_~ÅâÖêçìåÇ=~åÇ=íÜÉçêó=y − µ − δ ( y − µ ) − ... − δ ( y − µ ) = ω x + ω x + ... + ω x(2.6)t 1 t−1 nr t−nr 0 t 1 t−1ns t−ns=tÜÉå=ïÉ=áåíêçÇìÅÉ=íÜÉ=Ä~Åâï~êÇ=ëÜáÑí=çéÉê~íçê= B I=ÇÉÑáåÉÇ=ÄóW==B b yt yt − b= (2.7)=~åÇ=~ìíçêÉÖêÉëëáîÉ=~åÇ=ãçîáåÖ=~îÉê~ÖÉ=çéÉê~íçêë=çÑ=çêÇÉê= nr ~åÇ= ns I=ÇÉÑáåÉÇ=êÉëéÉÅíáîÉäó=ÄóW==2⎧ ⎪ = − 1 − 2 − −δ (B) 1 δ B δ B ... δnrB⎨2ns⎪⎩ ω(B) = 1+ ω1 B+ ω2B + ... + ωnsB=Éèì~íáçå=EOKSF=Å~å=ÄÉ=ïêáííÉå=ãçêÉ=ÉÅçåçãáÅ~ääó=~ëW==nr(2.8)δ (B) ỹ = ω(B)x(2.9)tt=çêW===ỹ −= δ1 (B) ω(B)x(2.10)t=ïÜÉêÉ=t~åÇ===(B) =ỹ =~êÉ=ÇÉîá~íÉë=çÑ=−1tyt=Ñêçã µ I=Θ δ (B) ω(B)(2.11)=áë=íÜÉ=íê~åëÑÉê=ÑìåÅíáçåK=tÜÉå=~=ëóëíÉã=Ü~ë=~=ÇÉä~óÉÇ=êÉëéçåëÉI=çê=ÇÉ~Ç=íáãÉ=çÑ=Çìê~íáçå= b I=íÜÉ=íê~åëÑÉê=ÑìåÅíáçå=ÄÉÅçãÉëW==−1Θ (B) = δ (B) ω(B)B b (2.12)=^äíÉêå~íáîÉäóI=EOKNMF=ã~ó=ÄÉ=ïêáííÉå=~ë=~=ëçJÅ~ääÉÇ=ÇáëÅêÉíÉ=Åçåîçäìíáçå=éêçÇìÅí=EëÉÉ=~äëç=ëÉÅíáçå=OKPKOFW==t∑∞∑ỹ = Θ x ≡ Θ x ≡ Θ(B) x ≡ ( Θ∗x)(2.13)t t−i i i t−i t ti=−∞ i=0=ïÜÉêÉ= Θt=áë=íÜÉ=íê~åëÑÉê=ÑìåÅíáçå=EÑáÖìêÉ=OKVFK=^oj^=íê~åëÑÉê=ÑìåÅíáçå=ãçÇÉäë=Å~å=ëÉêîÉ=~ë=ÅäçëÉ=~ééêçñáã~íáçåë=Ñçê=ã~åó=èìáíÉ=ÅçãéäáÅ~íÉÇ=Çóå~ãáÅ=ëóëíÉãëK=^é~êí=Ñêçã=íÜÉ=^oj^=ëíêìÅíìêÉI=ÜçïÉîÉêI=íïç=Ä~ëáÅ=~ëëìãéíáçåë=~êÉ=ã~ÇÉK=qÜÉ=Ñáêëí=áë=íÜÉ= tdelay free (MA) part exponential (AR) part01 2 3 45 6tfigure 2.9: Transfer function of a hypotheticalARMA(1,2) system with delay 1.==== PR=KKÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁKÁK