# What is difference between repeated poles and distinct poles? [duplicate]

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

• 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. Feb 26, 2020 at 7:21
• 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. Feb 26, 2020 at 7:23

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.