User:DukeEgr93/MagOrder

Question: for a transfer function

\( \begin{align} \Bbb{H}(j\omega)&=H(\omega)e^{j\theta(\omega)} \end{align} \)

what is the relationship between

\( \begin{align} \frac{d}{d\omega}\left(\left|\Bbb{H}(j\omega)\right|\right) \end{align} \)

and

\( \begin{align} \left|\frac{d}{d\omega}\left(\Bbb{H}(j\omega)\right)\right| \end{align} \)

Magnitude First

\( \begin{align} \frac{d}{d\omega}\left(\left|\Bbb{H}(j\omega)\right|\right)&= \frac{d}{d\omega}\left(\left|H(\omega)e^{j\theta(\omega)}\right|\right)\\ ~&=\frac{d}{d\omega}\left(H(\omega)\right) \end{align} \)

which makes sense since \(H\) is the magnitude of \(\Bbb{H}\).