there is error in the theory of line spectrum pair?
I'm studying the IEEE article "LINE SPECTRUM PAIR (LSP) AND SPEECH DATA COMPRESSION" by author FRANK K. SOONG and BIING-H WANG JUANG.they proved that the LSP is practical.but I doubt about the theory.
LPC inverse filter A(Z)=1+a1*Z^(-1)+a2*Z^(-2)+...+am*Z^(-m)
they proved that P(z) and Q(z) only have zeros on the unit circle if A(z) only have zeros inside the unit circle. they use a formula to prove the point,that is |Zi*Z-1|^2-|Z-Zi|^2=(1-|z|^2)*(1-|Zi|^2) Zi is constant and |Zi|<1
I think the formula in not correct,so i doubt about the theory of LSP.I know LSP is widely used in speech coding.anybody can help me?