Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have the transfer function$$ H(z) = \frac{z-.75}{.1 z+.15} $$

how do I find the Poles and Zeros?

share|improve this question
Poles are the values of $z$ where the denominator becomes zero; zeros are the values of $z$ where the numerator becomes, well, zero. I presume you know how to find the zeros of a linear function? –  J. M. Feb 3 '12 at 6:28
yes I do. So finding poles and zeros in the z domain is exactly like in the s-domain? –  skipfer0712 Feb 3 '12 at 6:29
Well, that is a function of $z$ in there, no? –  J. M. Feb 3 '12 at 6:34
I remember that one is not supposed to tag a question merely as homework, right? Perhaps complex-analysis can be applied? –  awllower Feb 3 '12 at 9:43

2 Answers 2

First of all, I'd advice to get rid of those awful decimal numbers and use fractions: $$H(z):=\frac{z-\frac{3}{4}}{\frac{1}{10}z+\frac{3}{20}}=\frac{\frac{1}{4}}{\frac{1}{20}}\frac{4z-3}{2z+3}=5\,\frac{4z-3}{2z+3}$$ From here, we clearly see the only zero of the function (i.e., exactly where its numerator vanishes) is $\,z=3/4\,$ , and its pole (i.e., exactly where the denominator vanishes) is $\,z=-3/2\,$, both simple.

share|improve this answer

roots of numerator are zeros and roots of denonumerator are poles

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.