Poles and Zeroes

Saturday, 4 May 2019

9:40 PM

We have seen that linear time invariant systems can be represented by their transfer functions (which are rational polynomials in ).

 

 

As both  and  are polynomials in , we can factor them to obtain

 

Where  Gain term

 

The zeroes are the roots of the number ()

The poles are the roots of the denominator ()

 

A system can be completely characterised by its N poles and M zeroes, and a gain term.

 

• Convey understanding visually
• Show system stability visually
• Give an idea of frequency response

 

 

On a s-plane (|jw _)

We represent POLES with X

We represent ZEROS with O