Poles and Zeros

Poles and zeros

For a transfer function $P(s)$ or $G[z]$, $\lambda \in \mathbb{C}$ is a:

• Zero if $P(\lambda )=0$ or $Z[lambeda]=0$
• Pole if $P(\lambda )=\infty$ or $Z[lambeda]=\infty$

Laplace / Continuous Time

• $H(s)$ has a pole at $s=a$ if $|H(a)|=\infty$
• $H(s)$ has a zero at $s=a$ if $|H(a)|=0$

Z-transform / Discrete Time

• $H[z]$ has a pole at $z=a$ if $|H(a)|=\infty$
• $H[z]$ has a zero at $s=a$ if $|H[a]|=0$

Poles: $x$ Zeros: $0$