EECE 340 Homework, Spring 2006

EECE 340-Signals and Systems Homework #6 Problem 1 Determine the Z-transform for each of the following sequences: a) x(n) =e"u(-n) b) x(n) =e"u(-n +1) c) x(n) =a"[u(n)-u(n- NJ] Problem 2 Determine the inverse for each of the Z-transforms listed below using the inversion formula, long division and partial fraction expansion whenever applicable: a) X(@)=—+,, T4352 I b) X(@)=—— 7» I+5z y-iz7 &) X(2)=——4-= 47 +42 +52 -! a) x@)=%, Zz -a 2 1 zZ>— z|> max (a), |o]) Page 1 of 1 | DB LECCE 32 40 Homework tt 6 Soby tire y) 7 A-~X¢t(hr)= 24 C-n) (6) oo Mlz)= Dé" =) (é'z)" n= — & fh=0 —_— | —_ —~ & i.e Ze? l2/ <e. L - BO) = er) =. |@ 2 ieee A= ~ — 2) A=6 _ sl 2 . | ele = —- 2 ; ry) C= a [acn) — elm ny] a 7 ~ VA) =X a2" =) el)” A= = ° _~iaN " =o = /-@2) ZN_ AN fgg) ne ; oN (za) = ta ay, ~ tas = » /2/>0 Ay [+412 } = —# —# | |}4+t2 -,27 -iz' J 2-2 ee, Ae lt —~z ye beh ge OK __lt 5-7 72 yy yn XCA) = Ch); NZ e oO J NZo Anverson formusa y= 2, lel>dt n-} ] xm = Lb Zz , _ dy Zee if JL Ee+d my). +4) —Ze -ZE-4y 2 Ya Lo IL ~~ oe? ~8A2_ (igh lé2F yt un MCA) = Cl , Ne-l oO / WN>o Tnvedeesn OV Mel a_ Mp) = -2_, Me KC) =l+ #21 -2 24 l+i27! f4+tgt CY = Fn) + Z (- ae tela i) - (ba (rt) - 2 a az er 1 —_ p-t2 f-a* _y| Zz aA pm at sol feat ,-% a a7 + C= a 2-2 oO [- a~y-t_ /— a —- 2 até as = fear) _- + ~ 273 a 0, NZO -l, N=0 a n4 Wt | =~ si -(4) 20-4 Yc tny ~ £50) ~ "Gy 7) (hI)