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A Pole at DC

Since both of the conditions

\begin{eqnarray*}
e^\tau ( 1 - \tau) &=& \cos(\nu)
\\
e^\tau &=& \frac{\sin(\nu)}{\nu}
\end{eqnarray*}

are clearly satisfied for $ \tau=\nu=0$ , we see that there is in fact a pole in the reflectance at dc ($ s=0$ ), provided it is not canceled by a zero at dc in the numerator $ N(s)$ .


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``Stability Proof for a Cylindrical Bore with Conical Cap'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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