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What is difference between repeated poles and distinct poles? As far as i am able to understand is that repeated poles are those that have same value of both x and y coordinates while distinct poles are those that have either same value of x coordinate or y coordinate but neither both

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  • $\begingroup$ um, we typically talk of "real" and "imaginary" part, not "x,y"; it helps a lot when you don't disconnect from the complex nature of these numbers, as they are solutions to a polynomial equation. $\endgroup$ Feb 26 '20 at 7:21
  • $\begingroup$ However, "distinct" is really just an English word, and means exactly what it means in English. Poles are distinct if they are not identical; done. $\endgroup$ Feb 26 '20 at 7:23
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Distinct poles do not need to share an x or y coordinate. They are classified as distinct as long as they do not share the same x AND y space. So any two poles are either distinct or repeated.

The effect repeated poles have on the impulse response of a filter is a little complicated, but the short answer is that it does change. This brief article describes the effects of repeated poles as well as providing proofs:

https://www.dsprelated.com/freebooks/filters/Repeated_Poles.html

Hope that helped.

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  • $\begingroup$ can you please kindly elaborate your answer with a photo/figure? $\endgroup$
    – engr
    Feb 26 '20 at 16:45
  • $\begingroup$ Which part would you like me to elaborate on? The location of the poles or the effect they have on the impulse response of a system? $\endgroup$
    – Jake
    Feb 26 '20 at 18:36
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    $\begingroup$ @Dan I said that it does change $\endgroup$
    – Jake
    Feb 27 '20 at 7:06
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    $\begingroup$ @engr every pole has a real and imaginary component to it (x and y, as you say). Lets say pole 1 is at (x1, y1) and pole 2 is at (x2, y2). If x1 = x2 and y1 = y2 then pole 1 and pole 2 are repeated. Essentially both poles are at the same location, which means they are repeated. If they aren't at the same place, x1 does not equal x2 or y1 doesn't equal y2, then they are distinct $\endgroup$
    – Jake
    Feb 27 '20 at 7:15
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    $\begingroup$ @Jake thanks- deleted my comment, not sure how I read it the other way $\endgroup$ Feb 27 '20 at 12:18

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