EENG 4308 Matlab 1 Name objectives, using Matlab to generate partial fractions e

Question

EENG 4308 Matlab 1 Name objectives, using Matlab to generate partial fractions expansion, put ratio of polyn omials in form suitable for partial fraction expansion, and use Matlab to generate pole zero diagrams. s +3 imple roots (real) Y(s) use residue operation in matlab s-2 Case 2 repeated roots (real Y(s) poly and then residue matlab operations Case 3 degree of numerator not less than degree of denominator (real roots) Y(e) use residue operation Case 4 complex use residue operation -& 20 Directions for presentation of information from Matlab All four cases wi require use of "residue" matlab operation nformation directly provided from Matlab on command line wi need to be reported. For each case use following format paying attention to specific notation ndicated here. [R1, P1, K1] residue (B, A) to be applied to each case any variable Note defined in a matlab program can be echoed to command window when desired All four cases will require a quantitative partial fractions interpretation in standard analytic form. definitely not Matlab format consistent either simple or repeated with that used to cases of roots latter appropriate for case 2) residue in All arrays regardless of it appearing numerator etc column or row format. on screen command window) Can reported in row format This is only to save space in this Case 2 will require use of poly command. report from matlab format poly (C) which will you Can use turn out to be consistent with subsequent use of residue command notation Final explicit instructions allow for generation of Pole zero plots with matlab generated output used in lieu of fill in by hand is FYI omputer not going to be acceptable When imply dash to fill in for omputer outputs inputs required in this report long string of zeros after decimal you can When computer outputs and should drop the zeros to save space e.g. computer out tputs 2.0000 place with 2

Explanation / Answer

%% R denotes residues and P denotes poles

(a)

n=[1 3];

d=[1 3 2];

[R,P,K]=residue(n,d)

R =

-1

2

P =

-2

-1

K =

[]

(b)

n=[1 -2];

d=[1 1 0];

[R,P,K]=residue(n,d)

R =

3

-2

P =

-1

0

K =

[]

(c)

n=[2 9 11 2];

d=[1 4 3];

[R,P,K]=residue(n,d)

R =

2

-1

P =

-3

-1

K =

2 1

(d)

n=[1 0];

d=[1 -8 20];

[R,P,K]=residue(n,d)

R =

0.5000 - 1.0000i

0.5000 + 1.0000i

P =

4.0000 + 2.0000i

4.0000 - 2.0000i

K =

[]

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