# When do we have a minimum phase couple

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?

## 1 Answer

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.

• Wonderful. Thanks a lot. I have spent two days trying to find why but did not consider the convention used by the book. I was going to drop the book for a modern alternative but I think I might crack on with it if I cannot find an alternative. Thanks a lot for saving me. – Chika May 26 '16 at 8:31
• @Chika: Have a look at this answer for two other great (and free) DSP books. – Matt L. May 26 '16 at 8:59
• @Chika you shall better drop the book anyway, what is the meaning of learning everthing with an opposite convention and then trying to map everything back to the other? – Fat32 May 26 '16 at 12:15
• @Fat32 Yeah good point, am gonna have to let it go. I also struggle with the some of the questions at the end of the chapters; with no way to check my answer since there are no solutions and the question seems to require Math that the chapters did not mention. – Chika May 26 '16 at 16:38