Difference between revisions of "User:DukeEgr93/MagOrder"
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\(
\begin{align}
\Bbb{H}(j\omega)&=H(\omega)e^{j\theta(\omega)}
\end{align}
\)
\(
\begin{align}
\frac{d}{d\omega}\left(\left|\Bbb{H}(j\omega)\right|\right)
\end{align}
\)
\(
\begin{align}
\left|\frac{d}{d\omega}\left(\Bbb{H}(j\omega)\right)\right|
\end{align}
\)
\(
\begin{align}
\frac{d}{d\omega}\left(\left|\Bbb{H}(j\omega)\right|\right)&=
\frac{d}{d\omega}\left(\left|H(\omega)e^{j\theta(\omega)}\right|\right)\\
~&=\frac{d}{d\omega}\left(H(\omega)\right)
\end{align}
\)
\(
\begin{align}
\left|\frac{d}{d\omega}\left(\Bbb{H}(j\omega)\right)\right|&=
\left|\frac{d}{d\omega}\left( H(\omega)e^{j\theta(\omega)} \right)\right|
\end{align}
\)
| Line 27: | Line 27: | ||
</math></center> | </math></center> | ||
which makes sense since <math>H</math> is the magnitude of <math>\Bbb{H}</math>. | which makes sense since <math>H</math> is the magnitude of <math>\Bbb{H}</math>. | ||
| + | |||
| + | == Derivative First == | ||
| + | |||
| + | <center><math> | ||
| + | \begin{align} | ||
| + | \left|\frac{d}{d\omega}\left(\Bbb{H}(j\omega)\right)\right|&= | ||
| + | \left|\frac{d}{d\omega}\left( H(\omega)e^{j\theta(\omega)} \right)\right| | ||
| + | \end{align} | ||
| + | </math></center> | ||
Revision as of 19:26, 20 November 2009
Question: for a transfer function
what is the relationship between
and
Magnitude First
which makes sense since \(H\) is the magnitude of \(\Bbb{H}\).
