Pole & Zero to Time Domain Response

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Animation shows the time-response of a signal represented by a set of poles and zeros in the s-domain. All the poles and zeros can be moved around to show in real time the effect in the time domain. Notice that if all the poles are in the open left hand plane (OLHP), the response decays to zero. Such a system is described as stable. Even a single pole in the right hand plane causes the system response to grow infinitely. Systems with such responses are unstable. Zeros change the output response, but do not affect stability. Animation generated by Mathematica code. Code available at

Aaron Becker
"Poles and Zeros of Time-Domain Response Functions"
Wolfram Demonstrations Project
Published: November 8 2016
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Would be even better with some explanations. For those who understand poles and zero plots and how they interact withbthe step response in the time domoin, it is for sure beautiful. For all others it's still a mistery.

patrickstrasser-mikhail
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I get what the poles do to the response but what do the zeros do to theresponse?

ElJefe
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one semester in control theory illustrated in 30sec 😊

charakable
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Ammazing, I should have had it at the time of my classes in the University.

fifaham
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Really great simulation, thanks a lot for sharing the video and specially the code.

suheladesilva
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Any chance you feel like sharing the code for this? Thanks.

Tyetheberious
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what a legend you are thank you so much!

whyaskpage
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Sir i just want which software did you used for this

akankshasrivastava
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Would have been helpful if you shared the code 😊

TheAnnaKarpinska