Characterizing Transfer Functions

The same characteristics can be used for both Discrete and Continuous Transfer Functions

A transfer function $P(s)$/$G[z]$ is

• rational if the numerator and denominators are both polynomials
• real if above AND all the coefficients are real
• proper if above and $deg(D)\ge deg(N)$
• strictly proper if above and $deg(D)>deg(N)$

Given an input signal $\lambda \in \mathbb{C}$ a transfer function is

• zero if $P(\lambda )/G[\lambda ]=0$
• pole if $P(\lambda )/G[\lambda ]=\infty$