Why does the Residue function returns complex coefficients of a rational function....??

Hi

Even though I ensured that all my poles ,residues are complex conjugate pairs and the direct term is real, the residue function returns complex coefficients. May I know the reason why this is happening in matlab.

For eg:

Poles=[ -0.297252868065168 - 11.6108351815607i -0.297252868065168 + 11.6108351815607i -19.9444674513931 - 8.76592887488931i -19.9444674513931 + 8.76592887488931i -8.52965151869893 - 23.6423888144931i -8.52965151869893 + 23.6423888144931i];

Res=[ -0.219160922557423 + 0.314530473001705i -0.219160922557423 - 0.314530473001705i 3.62282522955231 + 177.563841204173i 3.62282522955231 - 177.563841204173i -4.53489652493515 - 28.5303076418931i -4.53489652493515 + 28.5303076418931i];

Direct_term=0.00210679058580560;

[b a]=residue(Res,Poles,Direct_term);

Why am I getting complex co-eff in 'b' ?? Please let me know asap....

Thanks Venu

Answer 1

[the cyclist]

Looks to me that the imaginary parts are tiny, and are just computer round-off error.

[venu]

For the problem i stated above itz tiny but when i have 7 complex conjugate pairs I have significant imaginary number..

Poles=[

-0.235595796828570 - 7.51689426974672i

-0.235595796828570 + 7.51689426974672i

-0.781740831997082 - 8.52857663770894i

-0.781740831997082 + 8.52857663770894i

-0.944616475393567 - 10.2878136072271i

-0.944616475393567 + 10.2878136072271i

-3.08711512408251 - 9.90142234678996i

-3.08711512408251 + 9.90142234678996i

-0.297252868065168 - 11.6108351815607i

-0.297252868065168 + 11.6108351815607i

-19.9444674513931 - 8.76592887488931i

-19.9444674513931 + 8.76592887488931i

-8.52965151869893 - 23.6423888144931i

-8.52965151869893 + 23.6423888144931i];

Res=[

0.281061150197145 + 0.0578568842439584i

0.281061150197145 - 0.0578568842439584i

1.37371769852477 + 0.507158376975511i

1.37371769852477 - 0.507158376975511i

-0.0439844443484282 + 2.27379994030156i

-0.0439844443484282 - 2.27379994030156i

-5.70758424642157 - 21.3783127156549i

-5.70758424642157 + 21.3783127156549i

-0.219160922557423 + 0.314530473001705i

-0.219160922557423 - 0.314530473001705i

3.62282522955231 + 177.563841204173i

3.62282522955231 - 177.563841204173i

-4.53489652493515 - 28.5303076418931i

-4.53489652493515 + 28.5303076418931i];

Direct_term=0.00210679058580560;

[b a]=residue(Res,Poles,Direct_term);

Check this.. itzz more significant...

[Walter Roberson]

It would help if you could show the actual outputs you get. People do not always have MATLAB handy to run tests with at the time they are reading questions.

[venu]

The below are the numerator coefficients which is the output of the above code

b=[

0.00210679058580560 + 0.00000000000000i

-10.3135389504971 + 0.00000000000000i

669.131286493158 + 0.00000000000000i

-28627.7202535250 + 0.00000000000000i

734688.410571537 + 0.00000000000000i

-13659002.1713074 + 0.00000000000000i

245090589.254096 + 4.76837158203125e-07i

-2729141300.24354 + 7.62939453125000e-06i

37871334625.4884 - 7.62939453125000e-06i

-268822943451.791 + 0.00146484375000000i

3021233412244.70 + 0.00000000000000i

-12880358576851.8 - 0.0312500000000000i

120988980636702 + 0.125000000000000i

-239081416369462 - 0.437500000000000i

1.92634225464627e+15 + 1.75000000000000i];

please help

[the cyclist]

venu, when I run that code, I get that the largest imaginary part is 15 orders of magnitude smaller than the largest real part. I still believe this is roundoff error.

If you need better that this, then maybe you need to solve this analytically, and not numerically. I don't know for sure, but maybe the Symbolic Math Toolbox handles this.