I obtained this polynomial equations:

$$A(z) = 1 - 0.7987 z^{-1} - 0.125 z^{-2} - 0.511 z^{-3} + 0.06889 z^{-4} + 0.3465 z^{-5} + 0.4809 z^{-6} + 0.04951 z^{-7} - 0.5298 z^{-8} + 0.1828 z^{-9}$$

How do I plot the root of this polynomial equation? I want to observe how the roots are moving inside the system.


If the vector a contains the polynomial coefficients, you can compute the roots of the polynomial by

r = roots(a);

And then you can plot those roots as points in the complex plane with some marker (e.g., 'x'):


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  • $\begingroup$ one more thing, what is the difference if i use 'roots' command and 'nyquist' command in Matlab? because it seems like i cannot see the behaviour of the root. when i plot, it just show me a line. any idea on what i can use to see the root's behaviour if i have about 3 system. i want to observe the root's behaviour for each system. $\endgroup$ – Hakd Jul 2 '15 at 13:46
  • $\begingroup$ @Hakd: You shouldn't see a line but points in the complex plane where the roots of the polynomial are. But I'm not so sure anymore what you really want, because a Nyquist plot is a totally different thing. A Nyquist plot shows you the complex frequency response as a function of frequency. $\endgroup$ – Matt L. Jul 2 '15 at 15:24
  • $\begingroup$ thanks sir! now i got it. how can i plot the unit circle within the root sir? $\endgroup$ – Hakd Jul 3 '15 at 2:32
  • $\begingroup$ @Hakd: check out the command zplane. $\endgroup$ – Matt L. Jul 3 '15 at 6:52

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