Wiley signals and systems e book TLFe BO 346

2 -3 -2 - IT - - * k iii igrirc 13.8: Series alk] ohtaiiircl from X ( z ) i i t E x a m p l ~13.7 (13.2%) has two iiiimcwtor zeros (poles) outside the oiigiri of the cornplrx plarw: zL 2.5: + : gives z p l = 51 , uxp2 - As the rcgiori of corrvrrgenct lies outszdr a circlc arountl the origin, we exp riglit-mirtl series r [ k ]= Z ' { X ( possiblr to esprc'ss X(zj as the f two terms (like (13.5j) my' can term an (~xponc~iltirzl oscillation Diiect partial fraction expansion does nut lead t o the goal a \ it prodiiccs ;t b ~ i i ^of ~ i the form (13.30) to cictrmiinr the exponeIit,ial teririi Hcre it helps to expmd X ( :)/z ir'ractions, instcad of X (2) into partial (13.31) Determining t h~ partial fractioii cocfficienls for exarnplr by cqiiating coefficients I r ~ d str) Ro = 1, 6'1 = -2 a d B2 = Multiplying b) t and trrm-b~ icrin iriversion aided by Exainplr 13.2 yields the series (13.32)