\dspSignal{x 0 eq {0}{x cvi 2 mod abs -1 exch exp x div} ifelse}
\end{dspPlot}
\end{figure}
\end{center}
\end{frame}
\begin{frame}\frametitle{Digital differentiator}
\begin{itemize}
\item the digital differentiator is again an ideal filter!
\item many approximations exist, with different properties
\end{itemize}
\end{frame}
\begin{frame}\frametitle{Wrap up}
\begin{itemize}
\item Continuous-time processing of discrete-time sequences
\item Discrete-time processing of continuous-time signals
\item Jumping back and forth using sampling and interpolation
\item In practice: Many applications of processing continuous-time signals in discrete time!
\end{itemize}
\end{frame}
\note{exercise: take the "standard" first difference approximation to the derivative y[n] = x[n]-x[n-1]/2 and compute the difference in magnitude for the frequency response wrt the ideal differentiator at $\omega=0.9\pi$}