Question

2. For the transfer functions in problem 1 (a)(d)(e), find the corresponding impulse response functions h(t) using partial fraction expansion and determine the value of lim h(t) if the limit exists. Verify that lim- n(t)-0 for stable systems. (optional) After performing the partial fraction expansion by hand (required), yoiu are encouraged to use MATLAB to verify your results. MATLAB has a function called 'residue' that can calculate poles (pi) and residues (ci). For example, the following line will calculate the residues and poles for problem 1.b >>[c, pl-residue([1 2],[1 5 8 4]) -1.0000 0.0000 1.0000 2.0000 -2.0000 -1.0000 35|+ 2 2 4 4556 5s +27- 2

Answer 1

4) 13 0.25 HCS) = uCk e. eーで

S 48+8+4 4 4 ご 19st 51 ナC 51-17 S+4 4と eu 4

KS CS+5) 2 5 쇼5 laplace hel Appl Sk In den af Hence fla dgutem J undta bla

a)

Verifiication by matlab:

>> a=[1 2 5]
a =

1 2 5

>> [r,p,k]=residue(b,a)
r =

0.00000 - 0.25000i
0.00000 + 0.25000i

p =

-1 + 2i
-1 - 2i

k = [](0x0)

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d)

Verifiication by matlab:

>> [r,p,k]=residue(b,a)
r =

-1.00000 + 0.00000i
0.50000 - 6.50000i
0.50000 + 6.50000i

p =

-4.00000 + 0.00000i
0.00000 + 1.00000i
-0.00000 - 1.00000i

k = [](0x0)

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e)

\Verifiication by matlab: