When do we have a minimum phase couple

Question

I am a DSP newbie and I am really confused after reading Chapter two of

"An Introduction to Digital Signal Processing by J. H. Karl".

On page 32, first paragraph, the book defines a minimum phase couplet as one with zeros OUTSIDE the unit circle of the z-plane. But I have read everywhere else that a minimum phase system has all zeros and poles INSIDE the unit circle.

Is this a contradiction? When do we have a minimum phase couplet?

Answer 1

The book uses the convention that $Z$ represents a unit delay (this is explained on this page). The more common convention is to denote the unit delay by $z^{-1}$. Consequently, minimum-phase systems have all their zeros inside the unit circle of the $z$-plane, but outside the unit circle of the $Z$-plane.