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hello,everyone
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)
P(z)=A(z)+A(Z^(-1))*Z^(-m-1)
Q(z)=A(z)-A(Z^(-1))*Z^(-m-1)

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?

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