I am trying to find the original reference for a lemma attributed to Cohn (as in Schur-Cohn method):



> 
> Let $A(z)$ be a palindromic or skew-palindromic polynomial, and denote its derivative by $A'(z)$. Then $A(z)$ and $A'(z)$ have the same number of zeros outside the unit circle.
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> 
> 


The lemma can be found at <http://www2.ece.ohio-state.edu/~randy/publications/RLM_journal/J11.pdf>, statement on p. 105, proof on p. 116, but I don't see a reference there. I presume that if I could find the historical papers on the Schur-Cohn method it would not be hard to find, but I am not having much luck with that so far.


(BTW, I am including the signal-analysis tag because this result seems to appear in the signal processing literature).



A palindromic polynomial and its derivative have the same number of zeros outside the unit circle. Reference?
MR0058748 (15,419a) 


Ancochea, Germán, Zeros of self-inversive polynomials,
Proc. Amer. Math. Soc. 4, (1953) 900–902. 
41.1X 


This is a simple and elegant proof of a theorem of A. Cohn [Math. Z. 14, 110–148 (1922)]. A polynomial $g(z)$ with its zeros symmetric with respect to the unit circle $C$ has the same number of zeros outside $C$ as its derivative $g′(z)$. The proof uses only Rouché's theorem and the continuity of the zeros of a polynomial as functions of its coefficients.


Reviewed by F. F. Bonsall


The Cohn reference is given in full as A. Cohn, Über die Anzahl der Wurzeln einer algebraischen Gleichung in einer Kreise, Math. Zeit. vol. 14 (1922) pp. 110-148. MR1544543


From another review, it seems there is also a proof in Marden's book, Geometry of polynomials, second edition, pp. 198–206. 


