EECE 340 Homework, Spring 2004

EECE 340-Signals and Systems Homework #4 Problem 1 Consider the unstable system whose transfer function, H(s), is given by: H(s)= =! , -l<ao<0. s(s+I) (a) Determine the impulse response of the system. (b) Determine the differential equation of the system (c) Determine the Direct form I and Direct form II block diagram representation of the system. Problem 2 Repeat problem # 1 for the causal system with transfer funcion given by: H ( Ss ) = 6 (st+2)(s+3) Problem 3 Repeat problem # | for the causal systems with transfer functions given by: H(s)= 28+3 (s+2)(s+3) and H(sj= 2s +3 (s+2)(s+3)(s-1) For question (a), use partial fraction expansion and also the Laplace inversion formula. H(s) =—= | -l<7<o, see Misr hes arog id “Stine H ls) Was ar Glen Canvelgence. Eden ye sttejo tn The g, L not sh tal) it Me S-— plane, fhon He 5 Sem es At carol, Hente, td AEintat, aa seaeng SOL Laplace avs Fart<o, Riy=_e™ S-+l =P>f (Lt) = E430 I, t<o — G()_ -! (5) His) Fig st as = G(s)[s+s] = —F(S) —» a3) , dely __ Pt) for L<o, Al) =o —pK(t) = Cen ye ©) Hy “Stee ~ =e <> GO 4 oe, yey a2 dfs (+.4)(5+3)(o-4P =_A Be D (542) " (5+3) © (s-* “(si A = of S+ 3 | ot (5+ H5—1)* Sag g B — _~S4+3 | _ 3 (S42) (S-y)* s-., — A543 _ & (542) (5+3) 1% . Via Larpteee tnveliten feral py = sea) dls ) 2H Jp (S42)(0+3) (s-)> an = Zitat AS =~ 4 — 3 , st 7 th fatto. = Gsrye |, (aura Cs+3)(s-)* Say Gaaiey| S=-3 ey eo As (54 2)(543) =| _ | ~#t 3 ~346 t =)-= ~s 5 io | 3 a7, < tT © TT Ss td0 o, tiLo (b) His) = L SHB SS GG) SF 85 389754 /2 F°(s) dle 4309) ~3 Aly _7 flew. > “Ge Se et op) - 3 dttt ” BP fe)