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$.

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