Miscellaneous Properties

• If all poles and zeros of a PR function are on the unit circle, then they alternate along the circle. Since this property is preserved by the bilinear transform, it is true in both the $s$ and $z$ planes. It can be viewed as a consequence of the $\pm 90\degrees$ phase bounds for positive-real functions.

• If $B(s)/A(s)$ is PR, then so is $B^\prime(s)/A^\prime(s)$ , where the prime denotes differentiation in $s$ .