Undergrad Polynomial Division: Solve with Mike's Help!

[MikeSv]

Hello everyone.

Iam working on a course in digital control systems and by reading my textbook I stumbled over this expression.

C(z) = 0.3678z + 0.2644 : z^2 − 1.3678z + 0.3678
= 0.3678z^−1 + 0.7675z^−2 + 0.9145z^−3 + ...

Now Iam wondering how the result of the polynomial division is obtained?

I tried long division but I am not able to get the same result.

Any help would be great.

Thanks in advance,

Mike

Ps. Sorry for not using the editor as Iam writing from a. Mobile device

 

[Buzz Bloom]

I tried long division but I am not able to get the same result.

Hi Mike:

I think long division is the right approach. It might help me help you if you would show the details of the long division you did.

Regards,
Buzz

 

[MikeSv]

Hi again and thanks for your reply.

I just looked at the factional again and now Iam not sure anymore if long division works as the power of the denominator is higher than the power of the numerator.

Cheers,

Mike

 

[Mark44]

Hi again and thanks for your reply.

I just looked at the factional again and now Iam not sure anymore if long division works as the power of the denominator is higher than the power of the numerator.

Cheers,

Mike

Yes, it still works. The first term of the dividend (the thing being divided) is .3678z, and the first term of the divisor is z², so the first term in the quotient will be .3678*$\frac 1 z$ or .3678z^-1. Just continue the process as usual for polynomial division.

 

[MikeSv]

Hello again and thanks for all the replies.

I finally found my mistake.

I took z^-2 instead of z^2 in The second term:-(

Now I have the correct result which looks like a power series.

Thanks again,



Mike