Pole–zero plot

In mathematics and signal processing, a pole/zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as:

• stability
• causal / anticausal
• region of convergence (ROC)
• minimum phase / non minimum phase

In general, a rational transfer function has the form:

$X(z)={\frac {P(z)}{Q(z)}}$

where

• $P(z)=0$ are the zeros of the system
• $Q(z)=0$ are the poles of the system