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Laplace Analysis of Trapezoidal Rule

The $ z$ transform of the trapezoid rule yields

\begin{eqnarray*}
F(z)=\frac{2m}{T}\frac{1-z^{-1}}{1+z^{-1}}V(z)
\end{eqnarray*}

Since $ F(s) = ms\,V(s)$ , the $ s$ to $ z$ mapping has become

$\displaystyle \zbox{s\to\frac{2}{T}\frac{1-z^{-1}}{1+z^{-1}}}
$

which is of course the standard bilinear transform:


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``Introduction to Physical Signal Models'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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